OFFSET
1,1
COMMENTS
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.
There are exactly 130 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..130
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) = 1082744062322 because it is the smallest number whose sum of proper divisors is equal to 666304038394: 1 + 2 + 13 + 26 + 41644002397 + 83288004794 + 541372031161 = 666304038394.
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
Anton Mosunov, May 22 2017
STATUS
approved