A287251 Numbers whose sum of proper divisors is equal to 666304038394.

1082744062322, 1178845606262, 1207676069426, 1215025011014, 1279464378926, 1309091462678, 1309893165362, 1310880770114, 1312211013242, 1315226230958, 1317231828218, 1318629668702, 1324707235382, 1325469101618, 1326419490542, 1328065089458, 1328085645914

Offset: 1

Author

Anton Mosunov, May 22 2017

Keywords

• fini
• full
• nonn

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).

Examples

			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.
		

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.

Crossrefs

Cf. A001065, A283156, A283157, A287233, A287238, A287247, A287262.