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

1,2

Links

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

Example

Sigma(3)=2^2, sigma(7)=2^3, sigma(21)=2^5, sigma(66)=2^4*3^2.

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);

Mathematica

sigmaPowerQ[1] = True; sigmaPowerQ[n_] := Min@FactorInteger[DivisorSigma[1, n]][[;; , 2]] > 1; DivisorSigma[1, #] & /@ Select[Range[400], sigmaPowerQ] (* Amiram Eldar, Sep 08 2019 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (ispowerful(s=sigma(n)), print1(s, ", ")); ); } \\ Michel Marcus, Sep 08 2019

Crossrefs

Cf. A001694, A000203, A180090, A180097.

Sequence in context: A094502 A162459 A129195 * A124143 A173617 A034041

Adjacent sequences: A180095 A180096 A180097 * A180099 A180100 A180101

Keyword

easy,nonn

Author

Walter Kehowski, Aug 10 2010

Extensions

a(1) and more terms from Amiram Eldar, Sep 08 2019

Status

approved