A180097 - OEIS

%I #12 Sep 08 2019 02:51:58

%S 1,3,7,21,22,30,31,46,51,55,66,70,71,81,85,93,94,102,107,110,115,119,

%T 127,138,142,154,156,159,165,170,187,199,210,213,214,217,230,235,238,

%U 253,255,265,282,291,310,318,321,322,330,343,345,355,357,364,371,374

%N Numbers n such that sigma(n) is powerful.

%H Amiram Eldar, <a href="/A180097/b180097.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;

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

%o (PARI) isok(n) = ispowerful(sigma(n)); \\ _Michel Marcus_, Sep 08 2019

%Y Cf. A001694, A000203, A180090, A180098.

%K easy,nonn

%O 1,2

%A _Walter Kehowski_, Aug 10 2010

%E a(1) and more terms from _Amiram Eldar_, Sep 08 2019