A287233 - OEIS

%I #17 Jul 22 2017 09:00:48

%S 111223111970,119597953286,153690118286,162254892614,165823548554,

%T 170330251118,172618269242,173103606398,174143614538,174490283894,

%U 174816560918,174923620562,175023621326,175949944022,176622299474,176749123766,176986301486,177090301922

%N Numbers whose sum of proper divisors is equal to 88978489594

%C 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.

%C There are exactly 95 elements in the sequence.

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

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

%H Anton Mosunov, <a href="/A287233/b287233.txt">Table of n, a(n) for n = 1..95</a>

%H C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/aliquot.pdf">The first function and its iterates</a>, A Celebration of the Work of R. L. Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge U. Press, to appear.

%e 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.

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

%K fini,full,nonn

%O 1,1

%A _Anton Mosunov_, May 22 2017