A287247 Numbers whose sum of proper divisors is equal to 289697407994.

300629385430, 331082751976, 348602203870, 539890623754, 552235683634, 556381352806, 556523967562, 557844696646, 562012970938, 569170200598, 569518766962, 573004430386, 574282506778, 575462269366, 576199620754, 577107726658, 577305647026, 577419601138

Offset

1,1

Comments

The number 289697407994 is the 47th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 123 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).

Links

Anton Mosunov, Table of n, a(n) for n = 1..123

C. Pomerance, The first function and its iterates, A Celebration of the Work of R. L. Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge U. Press, to appear.

Example

a(1) = 300629385430, because it is the smallest number whose sum of proper divisors is equal to 289697407994: 1 + 2 + 5 + 10 + 11 + 22 + 55 + 110 + 2732994413 + 5465988826 + 13664972065 + 27329944130 + 30062938543 + 60125877086 + 150314692715 = 289697407994.

Crossrefs

Cf. A001065, A283156, A283157, A287233, A287238, A287251, A287262.

Sequence in context: A345864 A354070 A273936 * A172578 A172588 A172691

Adjacent sequences: A287244 A287245 A287246 * A287248 A287249 A287250

Keyword

fini,full,nonn

Author

Anton Mosunov, May 22 2017

Status

approved