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

Author

N. J. A. Sloane, Jun 17 2011

Keywords

• nonn
• easy

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

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

Crossrefs

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

Programs

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 *)

PARI

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

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