

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.


12



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
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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. [From 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 A090504
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



