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URL: https://oeis.org/A065827

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A065827
Sum of squares of divisors of square numbers.
6
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
OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from Harry J. Smith)
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
Sum_{k>=1} 1/a(k) = 1.06464520174524878494847955427968776606386158167258511428260450690334042955... - Vaclav Kotesovec, Sep 20 2020
n^4 < a(n) < k*n^4 for n > 1 where k = Pi^2/6 = 1.6449.... - Charles R Greathouse IV, Sep 29 2025
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 *)
f[p_, e_] := (p^(4*e + 2) - 1)/(p^2 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 35] (* Amiram Eldar, Sep 13 2020 *)
PROG
(SageMath) [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
Sequence in context: A353056 A203173 A194532 * A318036 A326164 A143843
KEYWORD
mult,nonn
AUTHOR
Vladeta Jovovic, Dec 06 2001
STATUS
approved