A180098 Sigma(A180097(n)), sum of divisors of A180097(n), numbers n such that sigma(n) is powerful.
1, 4, 8, 32, 36, 72, 32, 72, 72, 72, 144, 144, 72, 121, 108, 128, 144, 216, 108, 216, 144, 144, 128, 288, 216, 288, 392, 216, 288, 324, 216, 200, 576, 288, 324, 256, 432, 288, 432, 288, 432, 324, 576, 392, 576, 648, 432, 576, 864, 400, 576, 432, 576, 784, 432
Offset: 1
Examples
Sigma(3)=2^2, sigma(7)=2^3, sigma(21)=2^5, sigma(66)=2^4*3^2.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
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);
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Mathematica
sigmaPowerQ[1] = True; sigmaPowerQ[n_] := Min@FactorInteger[DivisorSigma[1, n]][[;; , 2]] > 1; DivisorSigma[1, #] & /@ Select[Range[400], sigmaPowerQ] (* Amiram Eldar, Sep 08 2019 *)
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PARI
lista(nn) = {for (n=1, nn, if (ispowerful(s=sigma(n)), print1(s, ", ")););} \\ Michel Marcus, Sep 08 2019
Extensions
a(1) and more terms from Amiram Eldar, Sep 08 2019