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A344082 a(n) = n * Sum_{d|n} tau(d)^3 / d, where tau(n) is the number of divisors of n. 0
1, 10, 11, 47, 13, 110, 15, 158, 60, 130, 19, 517, 21, 150, 143, 441, 25, 600, 27, 611, 165, 190, 31, 1738, 92, 210, 244, 705, 37, 1430, 39, 1098, 209, 250, 195, 2820, 45, 270, 231, 2054, 49, 1650, 51, 893, 780, 310, 55, 4851, 132, 920, 275, 987, 61, 2440, 247, 2370, 297, 370, 67, 6721, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..61.

FORMULA

G.f.: Sum_{k >= 1} tau(k)^3 * x^k/(1 - x^k)^2.

If p is prime, a(p) = 8 + p.

MATHEMATICA

a[n_] := n * DivisorSum[n, DivisorSigma[0, #]^3/# &]; Array[a, 61] (* Amiram Eldar, May 09 2021 *)

PROG

(PARI) a(n) = n*sumdiv(n, d, numdiv(d)^3/d);

(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, numdiv(k)^3*x^k/(1-x^k)^2))

CROSSREFS

Cf. A007429, A062369, A097988, A344043.

Sequence in context: A042395 A041210 A267340 * A042413 A041212 A257313

Adjacent sequences:  A344079 A344080 A344081 * A344083 A344084 A344085

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, May 09 2021

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)