A152218 Numbers k such that sigma_2(k)*sigma_1(k)/sigma_0(k) is a perfect square.

1, 4, 529, 2116, 2583, 3249, 3346, 6150, 10332, 12474, 12792, 12996, 28224, 38240, 59245, 85905, 91035, 103607, 142560, 176382, 212949, 236980, 249744, 343620, 360096, 364140, 379050, 414428, 450840, 751530, 787710, 788424, 851796, 1059474, 1132096, 1366407

Offset: 1

Author

Ctibor O. Zizka, Nov 29 2008

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..200 from Donovan Johnson)

Crossrefs

Cf. A000005, A000290, A000203, A001157, A140480, A144695.

Programs

Mathematica

fQ[n_] := IntegerQ[ Sqrt[ DivisorSigma[2, n] DivisorSigma[1, n]/DivisorSigma[0, n]]]; k = 1; lst = {}; While[k < 1132096, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst (* Robert G. Wilson v, Sep 10 2010 *)
Select[Range[137*10^4],IntegerQ[Sqrt[(DivisorSigma[2,#]DivisorSigma[ 1,#])/ DivisorSigma[ 0,#]]]&] (* Harvey P. Dale, Jun 18 2018 *)

PARI

isok(k) = {my(f = factor(k)); issquare(sigma(f, 2) * sigma(f) / numdiv(f));} \\ Amiram Eldar, Feb 01 2025

Formula

{k: A001157(k)*A000203(k)/A000005(k) in A000290}.

Extensions

Correct definition recovered by Jack Brennen

12 more terms from R. J. Mathar, Aug 25 2010

More terms from Robert G. Wilson v, Sep 10 2010