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A288418 a(n) = Sum_{d|n} d^2*A000593(n/d). 7
1, 5, 13, 21, 31, 65, 57, 85, 130, 155, 133, 273, 183, 285, 403, 341, 307, 650, 381, 651, 741, 665, 553, 1105, 806, 915, 1210, 1197, 871, 2015, 993, 1365, 1729, 1535, 1767, 2730, 1407, 1905, 2379, 2635, 1723, 3705, 1893, 2793, 4030, 2765, 2257, 4433, 2850, 4030 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative because this sequence is the Dirichlet convolution of A000290 and A000593 which are both multiplicative. - Andrew Howroyd, Jul 27 2018

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

L.g.f.: log(Product_{k>=1} (1 + x^k)^sigma(k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Jun 19 2018

MATHEMATICA

a[n_] := DivisorSum[n, Function[d, d^2*DivisorSum[n/d, If[OddQ[#], #, 0]&]] ];

Array[a, 50] (* Jean-Fran├žois Alcover, Jul 03 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, d^2*sigma(d>>valuation(d, 2))); \\ Michel Marcus, Jul 03 2017

CROSSREFS

Cf. A000290, A192065.

Sum_{d|n} d^k*A000593(n/d): A288417 (k=0), A109386 (k=1), this sequence (k=2), A288419 (k=3), A288420 (k=4).

Sequence in context: A166095 A166090 A065766 * A034170 A272809 A273204

Adjacent sequences:  A288415 A288416 A288417 * A288419 A288420 A288421

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, Jun 09 2017

STATUS

approved

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Last modified July 9 16:24 EDT 2020. Contains 335544 sequences. (Running on oeis4.)