A287246 Numbers whose sum of proper divisors is equal to 57939481594

77753398058, 94151657522, 98497118618, 105654348614, 107396027126, 107978124554, 112402593722, 112536300194, 113395841738, 113591877506, 113834039318, 113903752562, 114541896698, 114637401218, 114663447902, 114856499738, 115175241854, 115246892846, 115271202986

Offset

1,1

Comments

The number 57939481594 is the 44th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 94 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..94

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) = 77753398058, because it is the smallest number whose sum of proper divisors is equal to 57939481594: 1 + 2 + 7 + 14 + 49 + 98 + 6793 + 13586 47551 + 95102 + 116797 + 233594 + 332857 + 665714 + 817579 + 1635158 + 5723053 + 11446106 + 793402021 + 1586804042 + 5553814147 + 11107628294 + 38876699029 = 57939481594.

Crossrefs

Cf. A001065, A283156, A283157, A287233, A287238, A287247, A287251, A287262.

Sequence in context: A103617 A213334 A211417 * A022252 A034653 A289116

Adjacent sequences: A287243 A287244 A287245 * A287247 A287248 A287249

Keyword

fini,full,nonn

Author

Anton Mosunov, May 22 2017

Status

approved