A180097 Numbers n such that sigma(n) is powerful.

1, 3, 7, 21, 22, 30, 31, 46, 51, 55, 66, 70, 71, 81, 85, 93, 94, 102, 107, 110, 115, 119, 127, 138, 142, 154, 156, 159, 165, 170, 187, 199, 210, 213, 214, 217, 230, 235, 238, 253, 255, 265, 282, 291, 310, 318, 321, 322, 330, 343, 345, 355, 357, 364, 371, 374

Offset: 1

Author

Walter Kehowski, Aug 10 2010

Keywords

• easy
• nonn

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

Crossrefs

Cf. A001694, A000203, A180090, A180098.

Programs

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;

Mathematica

sigmaPowerQ[1] = True; sigmaPowerQ[n_] := Min@FactorInteger[DivisorSigma[1, n]][[;; , 2]] > 1; Select[Range[1000], sigmaPowerQ] (* Amiram Eldar, Sep 08 2019 *)

PARI

isok(n) = ispowerful(sigma(n)); \\ Michel Marcus, Sep 08 2019

Extensions

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