A069070 Numbers n such that n*sigma(n) is a perfect square.

1, 40, 81, 135, 216, 224, 400, 819, 1372, 3240, 3744, 4650, 6318, 18144, 21700, 27930, 30240, 32400, 32760, 69312, 71148, 91694, 111132, 174592, 175500, 185220, 215472, 241395, 278318, 293907, 327600, 336675, 362700, 386232, 515450, 958737

Offset: 1

Author

Benoit Cloitre, Apr 05 2002

Keywords

• easy
• nonn

Comments

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

Also n such that abundancy of n, sigma(n)/n is a rational square. - Michel Marcus, Oct 06 2013

See A230043, resp. A230538, for n whose abundancy is a rational cube, resp. fourth power. - M. F. Hasler, Nov 02 2013

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1896 (terms < 4*10^12, first 500 terms from Donovan Johnson)

Crossrefs

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

Cf. A008848, A027687 (subsequences).

Cf. also A230043, A230538.

Positions of 0's in A355929.

Programs

Mathematica

Select[Range[1000000],IntegerQ[Sqrt[# DivisorSigma[1,#]]]&] (* Harvey P. Dale, Dec 24 2012 *)

PARI

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

PARI

isok(n) = issquare(sigma(n)/n); \\ Michel Marcus, Oct 06 2013

Extensions

More terms from Rick L. Shepherd, Apr 07 2002