

A191831


a(n) = Sum_{i+j=n, i,j >= 1} tau(i)*sigma(j), where tau() = A000005(), sigma() = A000203().


2



0, 1, 5, 12, 24, 39, 60, 87, 113, 158, 189, 249, 286, 372, 402, 516, 545, 696, 709, 886, 912, 1125, 1110, 1401, 1348, 1674, 1654, 1992, 1906, 2390, 2226, 2735, 2648, 3141, 2926, 3705, 3346, 4069, 3898, 4604, 4223, 5282, 4707, 5757, 5426, 6326, 5754, 7269, 6324, 7669, 7230, 8468, 7556, 9456, 8240, 10018, 9320, 10748, 9621, 12246
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OFFSET

1,3


COMMENTS

This is Andrews's D_{0,1}(n).


LINKS

Table of n, a(n) for n=1..60.
George E. Andrews, Stacked lattice boxes, Ann. Comb. 3 (1999), 115130.


FORMULA

G.f.: (Sum_{k>=1} x^k/(1  x^k))*(Sum_{k>=1} k*x^k/(1  x^k)).  Ilya Gutkovskiy, Jan 01 2017


MAPLE

with(numtheory); D01:=n>add(tau(j)*sigma(nj), j=1..n1);
[seq(D01(n), n=1..60)];


MATHEMATICA

Table[Sum[DivisorSigma[0, j] DivisorSigma[1, n  j], {j, n  1}], {n, 60}] (* Michael De Vlieger, Jan 01 2017 *)


PROG

(PARI) a(n)=sum(i=1, n1, numdiv(i)*sigma(ni)) \\ Charles R Greathouse IV, Feb 19 2013


CROSSREFS

Cf. A000005, A000203.
Sequence in context: A100479 A018806 A101425 * A188182 A187210 A299901
Adjacent sequences: A191828 A191829 A191830 * A191832 A191833 A191834


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Jun 17 2011


STATUS

approved



