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%I #9 Sep 08 2019 04:35:33
%S 1,4,8,32,36,72,32,72,72,72,144,144,72,121,108,128,144,216,108,216,
%T 144,144,128,288,216,288,392,216,288,324,216,200,576,288,324,256,432,
%U 288,432,288,432,324,576,392,576,648,432,576,864,400,576,432,576,784,432
%N Sigma(A180097(n)), sum of divisors of A180097(n), numbers n such that sigma(n) is powerful.
%H Amiram Eldar, <a href="/A180098/b180098.txt">Table of n, a(n) for n = 1..10000</a>
%e Sigma(3)=2^2, sigma(7)=2^3, sigma(21)=2^5, sigma(66)=2^4*3^2.
%p emin := proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z->z[2],L); min(L) else 0 fi end: L:=[]: for w to 1 do for n from 1 to 144 do sn:=numtheory[sigma](n); if emin(sn)>1 then L:=[op(L),n]; print(n,ifactor(n),sn,ifactor(sn)) fi; od; od; L; map(numtheory[sigma],L);
%t sigmaPowerQ[1] = True; sigmaPowerQ[n_] := Min@FactorInteger[DivisorSigma[1, n]][[;; , 2]] > 1; DivisorSigma[1, #] & /@ Select[Range[400], sigmaPowerQ] (* _Amiram Eldar_, Sep 08 2019 *)
%o (PARI) lista(nn) = {for (n=1, nn, if (ispowerful(s=sigma(n)), print1(s, ", ")););} \\ _Michel Marcus_, Sep 08 2019
%Y Cf. A001694, A000203, A180090, A180097.
%K easy,nonn
%O 1,2
%A _Walter Kehowski_, Aug 10 2010
%E a(1) and more terms from _Amiram Eldar_, Sep 08 2019
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