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%I #11 Oct 30 2022 21:28:55
%S 3,7,21,22,31,66,70,81,93,94,102,110,115,119,127,142,159,170,187,210,
%T 214,217,265,282,310,322,343,345,357,364,381,382,385,400,472,497,510,
%U 517,527,642,651,679,690,710,714,742,745,770,782,795,820,862,884,889
%N Numbers n such that sigma(n) is a nontrivial power, i.e., sigma(n) = a^b where a and b are greater than 1.
%C Probably an unsolved problem: what numbers can appear as bases in the representations of sigma(n) as nontrivial powers?
%C A175432(a(n)) > 1 for n >= 1. - _Jaroslav Krizek_, May 10 2010
%H Charles R Greathouse IV, <a href="/A065496/b065496.txt">Table of n, a(n) for n = 1..10000</a>
%e sigma(21) = 2^5, sigma(22) = 6^2, sigma(94) = 12^2.
%t 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 *)
%o (PARI) is(n)=ispower(sigma(n)) \\ _Charles R Greathouse IV_, Mar 09 2014
%Y Cf. A000203, A046528.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Nov 24 2001
%E More terms from _Vladeta Jovovic_, Nov 25 2001
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