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%I #8 Sep 16 2020 06:08:56
%S 66,70,102,210,282,364,400,510,642,690,714,770,820,930,966,1080,1092,
%T 1146,1164,1200,1416,1566,1624,1672,1782,2130,2226,2250,2346,2460,
%U 2530,2586,2652,2860,2910,2912,3012,3198,3210,3340,3498,3522,3560,3710,3810
%N Abundant numbers n such that sigma(n) is a perfect power.
%C Positive integers n such that sigma(n)>2*n and sigma(n)=a^b where both a and b are greater than 1.
%C If n is a term with sigma(n) a square, and p and q are members of A066436 that do not divide n, then n*p*q is in the sequence. Thus if A066436 is infinite, so is this sequence. - _Robert Israel_, Oct 29 2018
%H Robert Israel, <a href="/A124142/b124142.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=66 since sigma(66)=144=12^2.
%p 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:=[]: 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]; fi od od;
%t filterQ[n_] := With[{s = DivisorSigma[1, n]}, s > 2n && GCD @@ FactorInteger[s][[All, 2]] > 1];
%t Select[Range[4000], filterQ] (* _Jean-François Alcover_, Sep 16 2020 *)
%Y Cf. A001597, A005101, A065496, A066436.
%K nonn
%O 1,1
%A _Walter Kehowski_, Dec 01 2006
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