

A288417


a(n) = Sum_{dn} A000593(n/d).


12



1, 2, 5, 3, 7, 10, 9, 4, 18, 14, 13, 15, 15, 18, 35, 5, 19, 36, 21, 21, 45, 26, 25, 20, 38, 30, 58, 27, 31, 70, 33, 6, 65, 38, 63, 54, 39, 42, 75, 28, 43, 90, 45, 39, 126, 50, 49, 25, 66, 76, 95, 45, 55, 116, 91, 36, 105, 62, 61, 105, 63, 66, 162, 7, 105, 130, 69
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OFFSET

1,2


COMMENTS

Multiplicative because this sequence is the Dirichlet convolution of A000012 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)/k)) = Sum_{n>=1} a(n)*x^n/n.  Ilya Gutkovskiy, Jun 19 2018


PROG

(PARI) a(n)={sumdiv(n, d, sigma(d>>valuation(d, 2)))} \\ Andrew Howroyd, Jul 27 2018


CROSSREFS

Cf. A000012.
Sum_{dn} d^k*A000593(n/d): this sequence (k=0), A109386 (k=1), A288418 (k=2), A288419 (k=3), A288420 (k=4).
Sequence in context: A308021 A191707 A192177 * A159016 A289108 A246364
Adjacent sequences: A288414 A288415 A288416 * A288418 A288419 A288420


KEYWORD

nonn,mult


AUTHOR

Seiichi Manyama, Jun 09 2017


STATUS

approved



