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

Author

Joseph L. Pe, Nov 24 2001

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A000203, A046528.

Programs

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 *)

PARI

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

Extensions

More terms from Vladeta Jovovic, Nov 25 2001