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

1,1

Comments

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

Links

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A306359 A351542 A044870 * A151713 A224667 A118781

Adjacent sequences: A248018 A248019 A248020 * A248022 A248023 A248024

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 29 2014

Status

approved