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Number

1,729

1729 — The Hardy-Ramanujan Number

1,729 is a composite number, odd, a calendar year.

1729 is the famous taxicab number, the smallest number expressible as the sum of two positive cubes in two different ways:

\(1729 = 1^3 + 12^3 = 9^3 + 10^3\)

The story comes from G. H. Hardy visiting the ailing Ramanujan in hospital. Hardy remarked that he had arrived in cab number 1729, which seemed rather a dull number. Ramanujan immediately replied that, on the contrary, it was a very interesting number — the smallest expressible as the sum of two cubes in two different ways.

Sources https://en.wikipedia.org/wiki/1729_(number)
Arithmetic Number Carmichael Number Curated Deficient Number Gapful Number Harshad / Niven Odious Number Pernicious Number Recamán's Sequence Sphenic Number Squarefree

Notable events — 1729 AD

  1. Nov 9 Spain, France, and Britain sign the Treaty of Seville.
  2. May 20 Frederick the Great's flute lessons begin.
  3. Undated Bach composes the Brandenburg Concertos (collected and dated 1721, presented across years).

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type
Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year
365
ISO weeks
52
Started on
Saturday
January 1, 1729
Ended on
Saturday
December 31, 1729
Friday the 13ths
1
One Friday the 13th this year.
Easter Sunday
April 17
Sunday, April 17, 1729
Decade
1720s
1720–1729
Century
18th century
1701–1800
Millennium
2nd millennium
1001–2000
Years ago
297
297 years before 2026.

In other calendars

Hebrew
5489 / 5490 AM
Rosh Hashanah falls in September/October.
Islamic Hijri
1141 / 1142 AH
Lunar calendar; year spans differ from Gregorian.
Chinese
Year of the zodiac:Earth zodiac:Rooster
Sexagenary cycle position 46 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
2272 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri
1107 / 1108 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian
1721 / 1722 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
1651 / 1650 Saka
Indian national calendar; year starts in March.

Properties

Parity
Odd
Digit count
4
Digit sum
19
Digit product
126
Digital root
1
Palindrome
No
Bit width
11 bits
Reversed
9,271
Recamán's sequence
a(1,198) = 1,729
Square (n²)
2,989,441
Cube (n³)
5,168,743,489
Divisor count
8
σ(n) — sum of divisors
2,240
φ(n) — Euler's totient
1,296
Sum of prime factors
39

Primality

Prime factorization: 7 × 13 × 19

Nearest primes: 1,723 (−6) · 1,733 (+4)

Divisors & multiples

All divisors (8)
1 · 7 · 13 · 19 · 91 · 133 · 247 · 1729
Aliquot sum (sum of proper divisors): 511
Factor pairs (a × b = 1,729)
1 × 1729
7 × 247
13 × 133
19 × 91
First multiples
1,729 · 3,458 (double) · 5,187 · 6,916 · 8,645 · 10,374 · 12,103 · 13,832 · 15,561 · 17,290

Sums & aliquot sequence

As consecutive integers: 864 + 865 244 + 245 + … + 250 127 + 128 + … + 139 117 + 118 + … + 130
Aliquot sequence: 1,729 511 81 40 50 43 1 0 — terminates at zero

Representations

In words
one thousand seven hundred twenty-nine
Ordinal
1729th
Roman numeral
MDCCXXIX
Binary
11011000001
Octal
3301
Hexadecimal
0x6C1
Base64
BsE=
One's complement
63,806 (16-bit)
In other bases
ternary (3) 2101001
quaternary (4) 123001
quinary (5) 23404
senary (6) 12001
septenary (7) 5020
nonary (9) 2331
undecimal (11) 1332
duodecimal (12) 1001
tridecimal (13) a30
tetradecimal (14) 8b7
pentadecimal (15) 7a4

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓆼𓍢𓍢𓍢𓍢𓍢𓍢𓍢𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian)
͵αψκθʹ
Mayan (base 20)
𝋤·𝋦·𝋩
Chinese
一千七百二十九
Chinese (financial)
壹仟柒佰貳拾玖
In other modern scripts
Eastern Arabic ١٧٢٩ Devanagari १७२९ Bengali ১৭২৯ Tamil ௧௭௨௯ Thai ๑๗๒๙ Tibetan ༡༧༢༩ Khmer ១៧២៩ Lao ໑໗໒໙ Burmese ၁၇၂၉

Digit at this position in famous constants

π — Pi (π)
Digit 1,729 = 2
e — Euler's number (e)
Digit 1,729 = 7
φ — Golden ratio (φ)
Digit 1,729 = 6
√2 — Pythagoras's (√2)
Digit 1,729 = 3
ln 2 — Natural log of 2
Digit 1,729 = 7
γ — Euler-Mascheroni (γ)
Digit 1,729 = 5

Also seen as

Unicode codepoint
ہ
Arabic Letter Heh Goal
U+06C1
Other letter (Lo)

UTF-8 encoding: DB 81 (2 bytes).

Hex color
#0006C1
RGB(0, 6, 193)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.6.193.

Address
0.0.6.193
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.6.193

Unspecified address (0.0.0.0/8) — "this network" placeholder.

Position in π

The digit sequence 1729 first appears in π at position 8,042 of the decimal expansion (the 8,042ordinal-suffix:nd digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.