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

1,1

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

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

Sequence in context: A233479 A368035 A186178 * A165987 A139573 A263205

Adjacent sequences: A287248 A287249 A287250 * A287252 A287253 A287254

Keyword

fini,full,nonn

Author

Anton Mosunov, May 22 2017

Status

approved