A124144 Perfect powers pp such that sigma(k) = pp for some abundant number k.

144, 216, 576, 784, 961, 1296, 1728, 1764, 2304, 2744, 3136, 3600, 3844, 4356, 5184, 6084, 7056, 7776, 8100, 9216, 11664, 12544, 13824, 14400, 15376, 15876, 17424, 19600, 20736, 21952, 24336, 27000, 28224, 32400, 34596, 36864, 38416, 39204, 41616, 44100, 46656, 50176

Offset

1,1

Links

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

Example

a(1) = 144 since sigma(66) = 144 > 2*66 = 132.

Maple

with(numtheory); egcd := proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z->z[2], L); return igcd(op(L)) else return 1 fi; end; L:=[]: P:={}: for w to 1 do for n from 1 to 10000 do s:=sigma(n); if s>2*n and egcd(s)>1 then print(n, s, ifactor(s)); L:=[op(L), n]; P:=P union {s}; fi od od; L; P;

Mathematica

ppQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1;
f[n_] := Module[{s = DivisorSigma[1, n]}, If[s > 2*n, s, Nothing]];
seq[max_] := Union[Select[Array[f, max], # < max && ppQ[#] &]]; seq[60000] (* Amiram Eldar, Mar 11 2024 *)

Crossrefs

Cf. A001597, A005101, A065496.

Sequence in context: A069701 A358666 A349064 * A276564 A061040 A159456

Adjacent sequences: A124141 A124142 A124143 * A124145 A124146 A124147

Keyword

nonn

Author

Walter Kehowski, Dec 01 2006

Extensions

a(32) inserted and more terms added by Amiram Eldar, Mar 11 2024

Status

approved