A068984 a(n) = Sum_{d|n} d*tau(d)^2.

1, 9, 13, 45, 21, 117, 29, 173, 94, 189, 45, 585, 53, 261, 273, 573, 69, 846, 77, 945, 377, 405, 93, 2249, 246, 477, 526, 1305, 117, 2457, 125, 1725, 585, 621, 609, 4230, 149, 693, 689, 3633, 165, 3393, 173, 2025, 1974, 837, 189, 7449, 470, 2214, 897

Offset: 1

Author

Vladeta Jovovic, Apr 01 2002

Keywords

• mult
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A062369, A060724, A064950.

Programs

Magma

[&+[d*#Divisors(d)^2: d in Divisors(n)]:n in [1..51]]; // Marius A. Burtea, Sep 15 2019

Mathematica

a[n_] := DivisorSum[n, # * DivisorSigma[0, #]^2 &]; Array[a, 100] (* Amiram Eldar, Sep 15 2019 *)

PARI

a(n) = sumdiv(n, d, d*numdiv(d)^2) \\ Michel Marcus, Jun 17 2013

Formula

Multiplicative with a(p^e) = (p^(e+3)-3*p^(e+2)+4*p^(e+1)-p-1+2*p^(e+3)*e-6*p^(e+2)*e+4*p^(e+1)*e+p^(e+3)*e^2-2*p^(e+2)*e^2+p^(e+1)*e^2)/(p-1)^3.