A343661 Sum of numbers of y-multisets of divisors of x for each x >= 1, y >= 0, x + y = n.

1, 2, 4, 7, 12, 19, 30, 46, 70, 105, 155, 223, 316, 443, 619, 865, 1210, 1690, 2354, 3263, 4497, 6157, 8368, 11280, 15078, 19989, 26296, 34356, 44626, 57693, 74321, 95503, 122535, 157101, 201377, 258155, 330994, 424398, 544035, 696995, 892104, 1140298, 1455080

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = Sum_{k=1..n} binomial(sigma(k) + n - k - 1, n - k).

Example

The a(5) = 12 multisets of divisors:
  {1,1,1,1}  {1,1,1}  {1,1}  {1}  {}
             {1,1,2}  {1,3}  {2}
             {1,2,2}  {3,3}  {4}
             {2,2,2}

Mathematica

multchoo[n_, k_]:=Binomial[n+k-1, k];
Table[Sum[multchoo[DivisorSigma[0, k], n-k], {k, n}], {n, 10}]

Crossrefs

Antidiagonal sums of the array A343658 (or row sums of the triangle).

Dominates A343657.

A000005 counts divisors.

A007318 counts k-sets of elements of {1..n}.

A059481 counts k-multisets of elements of {1..n}.

A343656 counts divisors of powers.

Cf. A000169, A000312, A009998, A062319, A067824, A143773, A146291, A176029, A184389, A285572, A326077, A327527, A334996, A343652, A343657.

Sequence in context: A100823 A102346 A333148 * A342229 A326080 A287525

Adjacent sequences: A343658 A343659 A343660 * A343662 A343663 A343664

Keyword

nonn

Author

Gus Wiseman, Apr 30 2021

Status

approved