A191831 a(n) = Sum_{i+j=n, i,j >= 1} tau(i)*sigma(j), where tau() = A000005(), sigma() = A000203().

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

Offset

1,3

Comments

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

From Omar E. Pol, Dec 08 2021: (Start)

Zero together with the convolution of A000005 and A000203.

Zero together with the convolution of A341062 and A024916.

Zero together with the convolution of the nonzero terms of A006218 and A340793.

a(n) is also the volume of a symmetric polycube which belongs to the family of symmetric polycubes that represent the convolution of A000203 with any other integer sequence, n >= 1. (End)

Links

Table of n, a(n) for n=1..60.

George E. Andrews, Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130.

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(n-j), j=1..n-1);
[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, n-1, numdiv(i)*sigma(n-i)) \\ Charles R Greathouse IV, Feb 19 2013

Crossrefs

Cf. A000005, A000203 A006218, A024916, A086718, A237593, A340793, A341062.

Sequence in context: A100479 A018806 A101425 * A365540 A188182 A187210

Adjacent sequences: A191828 A191829 A191830 * A191832 A191833 A191834

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 17 2011

Status

approved