A069070 - OEIS

%I #30 Jul 29 2022 09:52:43

%S 1,40,81,135,216,224,400,819,1372,3240,3744,4650,6318,18144,21700,

%T 27930,30240,32400,32760,69312,71148,91694,111132,174592,175500,

%U 185220,215472,241395,278318,293907,327600,336675,362700,386232,515450,958737

%N Numbers n such that n*sigma(n) is a perfect square.

%C Also n such that the squarefree part of n (A007913) equals the squarefree part of sigma(n), A355928.

%C Also n such that abundancy of n, sigma(n)/n is a rational square. - _Michel Marcus_, Oct 06 2013

%C See A230043, resp. A230538, for n whose abundancy is a rational cube, resp. fourth power. - _M. F. Hasler_, Nov 02 2013

%H Giovanni Resta, <a href="/A069070/b069070.txt">Table of n, a(n) for n = 1..1896</a> (terms < 4*10^12, first 500 terms from Donovan Johnson)

%t Select[Range[1000000],IntegerQ[Sqrt[# DivisorSigma[1,#]]]&] (* _Harvey P. Dale_, Dec 24 2012 *)

%o (PARI) for(n=1,1000000,if(issquare(n*sigma(n)),print1(n,",")))

%o (PARI) isok(n) = issquare(sigma(n)/n); \\ _Michel Marcus_, Oct 06 2013

%Y Cf. A000203, A000290, A007913, A064987, A355928.

%Y Cf. A008848, A027687 (subsequences).

%Y Cf. also A230043, A230538.

%Y Positions of 0's in A355929.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Apr 05 2002

%E More terms from _Rick L. Shepherd_, Apr 07 2002