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

1,2

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)

Mathematica

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

Prog

(PARI) for(n=1, 1000000, if(issquare(n*sigma(n)), print1(n, ", ")))
(PARI) isok(n) = issquare(sigma(n)/n); \\ Michel Marcus, Oct 06 2013

Crossrefs

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

Cf. A008848, A027687 (subsequences).

Cf. also A230043, A230538.

Positions of 0's in A355929.

Sequence in context: A317095 A039468 A181458 * A174052 A141528 A160282

Adjacent sequences: A069067 A069068 A069069 * A069071 A069072 A069073

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 05 2002

Extensions

More terms from Rick L. Shepherd, Apr 07 2002

Status

approved