

A294645


a(n) = Sum_{dn} d^(n+1).


8



1, 9, 82, 1057, 15626, 282252, 5764802, 134480385, 3486843451, 100048830174, 3138428376722, 107006334784468, 3937376385699290, 155572843119354936, 6568408508343827972, 295150156996346511361, 14063084452067724991010, 708236696816416252145973
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OFFSET

1,2


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..385
Eric Weisstein's World of Mathematics, Divisor Function


FORMULA

G.f.: Sum_{k>0} k^(k+1)*x^k/(1(k*x)^k).
L.g.f.: log(Product_{k>=1} (1  (k*x)^k)) = Sum_{k>=1} a(k)*x^k/k.  Seiichi Manyama, Jun 02 2019


PROG

(PARI) {a(n) = sigma(n, n+1)}
(PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k^(k+1)*x^k/(1(k*x)^k)))
(PARI) N=20; x='x+O('x^N); Vec(x*deriv(log(prod(k=1, N, 1(k*x)^k)))) \\ Seiichi Manyama, Jun 02 2019


CROSSREFS

Column k=1 of A308504.
Cf. A023882, A023887, A082245, A292312.
Sequence in context: A045741 A283498 A294956 * A308668 A308481 A041146
Adjacent sequences: A294642 A294643 A294644 * A294646 A294647 A294648


KEYWORD

nonn


AUTHOR

Seiichi Manyama, Nov 05 2017


STATUS

approved



