A065496 Numbers n such that sigma(n) is a nontrivial power, i.e., sigma(n) = a^b where a and b are greater than 1.

3, 7, 21, 22, 31, 66, 70, 81, 93, 94, 102, 110, 115, 119, 127, 142, 159, 170, 187, 210, 214, 217, 265, 282, 310, 322, 343, 345, 357, 364, 381, 382, 385, 400, 472, 497, 510, 517, 527, 642, 651, 679, 690, 710, 714, 742, 745, 770, 782, 795, 820, 862, 884, 889

Offset

1,1

Comments

Probably an unsolved problem: what numbers can appear as bases in the representations of sigma(n) as nontrivial powers?

A175432(a(n)) > 1 for n >= 1. - Jaroslav Krizek, May 10 2010

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

sigma(21) = 2^5, sigma(22) = 6^2, sigma(94) = 12^2.

Mathematica

Do[s = DivisorSigma[1, n]; If[ Position[ Union[ Transpose[ FactorInteger[s]] [[2]]], 1] != {{1}} && Union[ Mod[ Union[ Transpose[ FactorInteger[s]] [[2]]], Union[ Transpose[ FactorInteger[s]] [[2]]] [[1]]]] == {0}, Print[n]], {n, 2, 10^3} ] (* Robert G. Wilson v, Nov 26 2001 *)

Prog

(PARI) is(n)=ispower(sigma(n)) \\ Charles R Greathouse IV, Mar 09 2014

Crossrefs

Cf. A000203, A046528.

Sequence in context: A196035 A196038 A180097 * A322922 A018479 A335411

Adjacent sequences: A065493 A065494 A065495 * A065497 A065498 A065499

Keyword

nonn

Author

Joseph L. Pe, Nov 24 2001

Extensions

More terms from Vladeta Jovovic, Nov 25 2001

Status

approved