Term

Semiperfect Number

Some subset of the proper divisors sums to the number itself (6, 12, 18, 20, 24, 28, 30, 36, 40, …).

520 numbers tagged.

A semiperfect (or pseudoperfect) number equals the sum of some of its proper divisors. 20's proper divisors are 1, 2, 4, 5, 10, and 1 + 4 + 5 + 10 = 20 — semiperfect. Perfect numbers are the boundary case where all proper divisors are needed.

Every multiple of a semiperfect number is semiperfect, and every abundant number that fails to be semiperfect is called weird — a far rarer breed. Deficient numbers can never be semiperfect: their divisors don't sum high enough.

6 12 18 20 24 28 30 36 40 42 48 54 56 60 66 72 78 80 84 88 90 96 100 102 104 108 112 114 120 126 132 138 140 144 150 156 160 162 168 174 176 180 186 192 196 198 200 204 208 210 216 220 222 224 228 234 240 246 252 258 260 264 270 272 276 280 282 288 294 300 304 306 308 312 318 320 324 330 336 340 342 348 350 352 354 360 364 366 368 372 378 380 384 390 392 396 400 402 408 414 416 420 426 432 438 440 444 448 450 456 460 462 464 468 474 476 480 486 490 492 496 498 500 504 510 516 520 522 528 532 534 540 544 546 550 552 558 560 564 570 572 576 580 582 588 594 600 606 608 612 616 618 620 624 630 636 640 642 644 648 650 654 660 666 672 678 680 684 690 696 700 702 704 708 714 720 726 728 732 736 738 740 744 748 750 756 760 762 768 770 774 780 784 786 792 798 800 804 810 812

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