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A065827 Sum of squares of divisors of square numbers. 4
1, 21, 91, 341, 651, 1911, 2451, 5461, 7381, 13671, 14763, 31031, 28731, 51471, 59241, 87381, 83811, 155001, 130683, 221991, 223041, 310023, 280371, 496951, 406901, 603351, 597871, 835791, 708123, 1244061, 924483, 1398101, 1343433, 1760031, 1595601, 2516921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..500

FORMULA

Multiplicative with a(p^e) = (p^(4*e+2)-1)/(p^2-1).

a(n) = A001157(n^2). - R. J. Mathar, Mar 31 2011

Dirichlet g.f. zeta(s)*zeta(s-2)*zeta(s-4)/zeta(2s-4). Dirichlet convolution of A001159 by the arithmetic function with terms n^2*A008966(n). - R. J. Mathar, Mar 31 2011

Sum_{k=1..n} a(k) ~ 189 * Zeta(3) * Zeta(5) * n^5 / Pi^6. - Vaclav Kotesovec, Feb 01 2019

MAPLE

A065827 := proc(n) numtheory[sigma][2](n^2) ; end proc:

seq(A065827(n), n=1..20) ; # R. J. Mathar, Apr 01 2011

MATHEMATICA

DivisorSigma[2, #]&/@(Range[40]^2) (* Harvey P. Dale, May 18 2011 *)

PROG

(Sage) [sigma(n^2, 2)for n in range(1, 34)] #  Zerinvary Lajos, Jun 13 2009]

(PARI) { for (n=1, 500, a=sigma(n^2, 2); write("b065827.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 01 2009

CROSSREFS

Cf. A001157, A065764.

Sequence in context: A259758 A203173 A194532 * A318036 A326164 A143843

Adjacent sequences:  A065824 A065825 A065826 * A065828 A065829 A065830

KEYWORD

mult,nonn

AUTHOR

Vladeta Jovovic, Dec 06 2001

STATUS

approved

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Last modified August 7 06:02 EDT 2020. Contains 336274 sequences. (Running on oeis4.)