A068984 - OEIS

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

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OFFSET

1,2

LINKS

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

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.

MATHEMATICA

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

PROG

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

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