A248021 Perfect powers which are not coprime to the sum of their divisors.

196, 216, 441, 1000, 1521, 1728, 1764, 2744, 3249, 3375, 3969, 4900, 5832, 5929, 6084, 7056, 7776, 8000, 8649, 9604, 9801, 10648, 11025, 12321, 12544, 12996, 13689, 13824, 15376, 15876, 16641, 17576, 17689, 21952, 23716, 24025, 24336, 25921, 27000, 28224, 29241, 33124, 33489, 34596

Offset: 1

Author

Robert G. Wilson v, Sep 29 2014

Keywords

• nonn
• easy

Comments

Intersection of A001597 and A069059. - Michel Marcus, Oct 25 2014

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

PARI

for(n=1, 1e5, if(ispower(n), if(gcd(n, sigma(n)) > 1, print1(n, ", ")))) \\ Felix Fröhlich, Oct 25 2014