Tags
Each tag groups numbers that share a property or origin. Click any tag to browse its members.
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Numbers whose proper divisors sum to more than the number itself.
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Achilles Number 23 Powerful numbers that are NOT perfect powers (72, 108, 200, 288, 392, 432, 500, 648, 675, 800, …).Powerful numbers that are NOT perfect powers (72, 108, 200, 288, 392, 432, 500, 648, 675, 800, …).
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Carmichael Number 3 Composite numbers that pass Fermat's little theorem for every base coprime to them (561, 1105, 1729, 2465, 2821, 6601, 8911, …).Composite numbers that pass Fermat's little theorem for every base coprime to them (561, 1105, 1729, 2465, 2821, 6601, 8911, …).
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Catalan Number 8 The Catalan number sequence (1, 1, 2, 5, 14, 42, 132, …) — appears widely in combinatorics.The Catalan number sequence (1, 1, 2, 5, 14, 42, 132, …) — appears widely in combinatorics.
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Primes p such that p ± 4 is also prime (3, 7, 13, 19, 37, 43, 67, …).
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Curated 27 Numbers with hand-written editorial context covering cultural, historical, or technical significance.Numbers with hand-written editorial context covering cultural, historical, or technical significance.
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Deficient Number 10,857 Numbers whose proper divisors sum to less than the number itself — the most common kind.Numbers whose proper divisors sum to less than the number itself — the most common kind.
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Numbers of the form n! = 1 × 2 × … × n (1, 2, 6, 24, 120, 720, …).
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Fibonacci 18 Numbers in the Fibonacci sequence, where each term is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, …).Numbers in the Fibonacci sequence, where each term is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, …).
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Happy Number 1,718 Iterating the sum of squares of digits eventually reaches 1 (1, 7, 10, 13, 19, 23, 28, 31, 32, 44, …).Iterating the sum of squares of digits eventually reaches 1 (1, 7, 10, 13, 19, 23, 28, 31, 32, 44, …).
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Harshad / Niven 426 Numbers divisible by the sum of their decimal digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, …).Numbers divisible by the sum of their decimal digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, …).
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Figurate numbers k(5k−3)/2 (1, 7, 18, 34, 55, 81, 112, 148, …).
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Hexagonal 33 Figurate numbers k(2k−1) (1, 6, 15, 28, 45, 66, 91, 120, 153, …). Every hexagonal number is also triangular.Figurate numbers k(2k−1) (1, 6, 15, 28, 45, 66, 91, 120, 153, …). Every hexagonal number is also triangular.
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Kaprekar Number 8 Numbers whose square can be split into two parts that sum back to the original (297² = 88209 → 88 + 209 = 297).Numbers whose square can be split into two parts that sum back to the original (297² = 88209 → 88 + 209 = 297).
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Numbers in the Lucas sequence, a Fibonacci-like sequence starting with 2 and 1.
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Primes of the form 2^p − 1 where p is also prime (3, 7, 31, 127, 8191, …).
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Narcissistic / Armstrong 15 Numbers equal to the sum of their digits each raised to the power of the digit count (153 = 1³ + 5³ + 3³).Numbers equal to the sum of their digits each raised to the power of the digit count (153 = 1³ + 5³ + 3³).
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Figurate numbers k(3k−2) (1, 8, 21, 40, 65, 96, 133, 176, …).
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Numbers whose decimal digits read the same forwards and backwards.
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Figurate numbers k(3k−1)/2 (1, 5, 12, 22, 35, 51, 70, 92, …).
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Numbers that are the cube of an integer (0, 1, 8, 27, 64, 125, …).
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Perfect Number 3 Numbers equal to the sum of their proper divisors. Only eight are known under 2^63 (6, 28, 496, 8128, …).Numbers equal to the sum of their proper divisors. Only eight are known under 2^63 (6, 28, 496, 8128, …).
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Numbers that are the square of an integer (0, 1, 4, 9, 16, 25, …).
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Numbers of the form 10^k. Basis for decimal place value and metric prefixes.
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Numbers of the form 2^k. Fundamental to computing — bytes, bits, address spaces.
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Powerful Number 80 Every prime in the factorization appears with exponent ≥ 2 (1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, …).Every prime in the factorization appears with exponent ≥ 2 (1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, …).
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Prime 9,594 Prime numbers — natural numbers greater than 1 with no positive divisors other than 1 and themselves.Prime numbers — natural numbers greater than 1 with no positive divisors other than 1 and themselves.
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Pronic / Oblong 46 Numbers of the form k(k+1) — twice a triangular number (0, 2, 6, 12, 20, 30, 42, 56, …).Numbers of the form k(k+1) — twice a triangular number (0, 2, 6, 12, 20, 30, 42, 56, …).
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Repdigit 19 Numbers where every digit is identical (11, 22, 33, …, 111, 222, … — repunits are a subset).Numbers where every digit is identical (11, 22, 33, …, 111, 222, … — repunits are a subset).
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Numbers consisting only of 1s in decimal: 1, 11, 111, 1,111, 11,111, …
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Primes p such that p ± 6 is also prime — “sexy” from the Latin sex (six).
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Smith Number 84 Composite numbers whose digit sum equals the sum of digit sums of their prime factors (4, 22, 27, 58, 85, 94, 121, 166, …).Composite numbers whose digit sum equals the sum of digit sums of their prime factors (4, 22, 27, 58, 85, 94, 121, 166, …).
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Products of three distinct primes (30, 42, 66, 70, 78, 102, …).
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Square Pyramidal 16 Figurate numbers k(k+1)(2k+1)/6 — points stacked in a square pyramid (1, 5, 14, 30, 55, 91, 140, 204, 285, …).Figurate numbers k(k+1)(2k+1)/6 — points stacked in a square pyramid (1, 5, 14, 30, 55, 91, 140, 204, 285, …).
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Squarefree 10,554 Numbers not divisible by the square of any prime — every prime appears in the factorization at most once.Numbers not divisible by the square of any prime — every prime appears in the factorization at most once.
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Strobogrammatic 28 Numbers that look the same when rotated 180° (0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, …).Numbers that look the same when rotated 180° (0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, …).
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Tetrahedral 21 Figurate numbers k(k+1)(k+2)/6 — the count of balls stacked in a triangular pyramid (1, 4, 10, 20, 35, 56, 84, 120, 165, 220, …).Figurate numbers k(k+1)(k+2)/6 — the count of balls stacked in a triangular pyramid (1, 4, 10, 20, 35, 56, 84, 120, 165, 220, …).
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Triangular 65 Numbers of the form k(k+1)/2 — the count of dots forming an equilateral triangle (1, 3, 6, 10, 15, …).Numbers of the form k(k+1)/2 — the count of dots forming an equilateral triangle (1, 3, 6, 10, 15, …).
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Primes p such that p ± 2 is also prime (3, 5, 7, 11, 13, 17, 19, 29, 31, …).
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Numbers in a plausible calendar-year range (1 through 2100).
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time 2