A248021 - OEIS

%I #31 Apr 14 2020 04:27:45

%S 196,216,441,1000,1521,1728,1764,2744,3249,3375,3969,4900,5832,5929,

%T 6084,7056,7776,8000,8649,9604,9801,10648,11025,12321,12544,12996,

%U 13689,13824,15376,15876,16641,17576,17689,21952,23716,24025,24336,25921,27000,28224,29241,33124,33489,34596

%N Perfect powers which are not coprime to the sum of their divisors.

%C Intersection of A001597 and A069059. - _Michel Marcus_, Oct 25 2014

%H Amiram Eldar, <a href="/A248021/b248021.txt">Table of n, a(n) for n = 1..10000</a>

%t perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[ Range@ 35000, perfectPowerQ[ #] && GCD[#, DivisorSigma[1, #]] > 1 &]

%o (PARI) for(n=1, 1e5, if(ispower(n), if(gcd(n, sigma(n)) > 1, print1(n, ", ")))) \\ _Felix Fröhlich_, Oct 25 2014

%Y Cf. A001597 (perfect powers), A069059 (gcd(n, sigma(n)) != 1).

%K nonn,easy

%O 1,1

%A _Robert G. Wilson v_, Sep 29 2014