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 A069070 Numbers n such that n*sigma(n) is a perfect square. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also n such that the squarefree part of n equals the squarefree part of sigma(n). 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. 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

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Last modified August 2 08:47 EDT 2021. Contains 346422 sequences. (Running on oeis4.)