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

Author

Anton Mosunov, May 22 2017

Keywords

• fini
• full
• nonn

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).

Examples

			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.
		

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.

Crossrefs

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