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
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
(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
KEYWORD
mult,nonn
AUTHOR
Vladeta Jovovic, Dec 06 2001
STATUS
approved