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%I A065827 #30 Sep 20 2020 09:13:53
%S A065827 1,21,91,341,651,1911,2451,5461,7381,13671,14763,31031,28731,51471,
%T A065827 59241,87381,83811,155001,130683,221991,223041,310023,280371,496951,
%U A065827 406901,603351,597871,835791,708123,1244061,924483,1398101,1343433,1760031,1595601,2516921
%N A065827 Sum of squares of divisors of square numbers.
%H A065827 Amiram Eldar, <a href="/A065827/b065827.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from Harry J. Smith)
%F A065827 Multiplicative with a(p^e) = (p^(4*e+2)-1)/(p^2-1).
%F A065827 a(n) = A001157(n^2). - _R. J. Mathar_, Mar 31 2011
%F A065827 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
%F A065827 Sum_{k=1..n} a(k) ~ 189 * Zeta(3) * Zeta(5) * n^5 / Pi^6. - _Vaclav Kotesovec_, Feb 01 2019
%F A065827 Sum_{k>=1} 1/a(k) = 1.06464520174524878494847955427968776606386158167258511428260450690334042955... - _Vaclav Kotesovec_, Sep 20 2020
%p A065827 A065827 := proc(n) numtheory[sigma][2](n^2) ; end proc:
%p A065827 seq(A065827(n),n=1..20) ; # _R. J. Mathar_, Apr 01 2011
%t A065827 DivisorSigma[2,#]&/@(Range[40]^2) (* _Harvey P. Dale_, May 18 2011 *)
%t A065827 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 *)
%o A065827 (Sage) [sigma(n^2,2)for n in range(1,34)] # _Zerinvary Lajos_, Jun 13 2009
%o A065827 (PARI) { for (n=1, 500, a=sigma(n^2, 2); write("b065827.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 01 2009
%Y A065827 Cf. A001157, A065764.
%K A065827 mult,nonn
%O A065827 1,2
%A A065827 _Vladeta Jovovic_, Dec 06 2001

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