%I #13 May 22 2017 12:11:45
%S 1082744062322,1178845606262,1207676069426,1215025011014,
%T 1279464378926,1309091462678,1309893165362,1310880770114,
%U 1312211013242,1315226230958,1317231828218,1318629668702,1324707235382,1325469101618,1326419490542,1328065089458,1328085645914
%N Numbers whose sum of proper divisors is equal to 666304038394.
%C The number 666304038394 is the 48th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.
%C There are exactly 130 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="/A287251/b287251.txt">Table of n, a(n) for n = 1..130</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) = 1082744062322 because it is the smallest number whose sum of proper divisors is equal to 666304038394: 1 + 2 + 13 + 26 + 41644002397 + 83288004794 + 541372031161 = 666304038394.
%Y Cf. A001065, A283156, A283157, A287233, A287238, A287247, A287262.
%K fini,full,nonn
%O 1,1
%A _Anton Mosunov_, May 22 2017