A287233 Numbers whose sum of proper divisors is equal to 88978489594

111223111970, 119597953286, 153690118286, 162254892614, 165823548554, 170330251118, 172618269242, 173103606398, 174143614538, 174490283894, 174816560918, 174923620562, 175023621326, 175949944022, 176622299474, 176749123766, 176986301486, 177090301922

Offset

1,1

Comments

The number 88978489594 is the 45th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 95 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..95

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) = 111223111970, because it is the smallest number whose sum of proper divisors is equal to 88978489594: 1 + 2 + 5 + 10 + 11122311197 + 22244622394 + 55611555985 = 88978489594.

Crossrefs

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

Sequence in context: A095427 A038454 A288275 * A122717 A287238 A072718

Adjacent sequences: A287230 A287231 A287232 * A287234 A287235 A287236

Keyword

fini,full,nonn

Author

Anton Mosunov, May 22 2017

Status

approved