A236937 Number of partitions of n such that the parts include all primes, with multiplicity, dividing n.

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 1, 7, 1, 7, 15, 22, 1, 42, 1, 56, 56, 30, 1, 176, 176, 56, 385, 297, 1, 627, 1, 1002, 490, 176, 1255, 2436, 1, 297, 1255, 4565, 1, 5604, 1, 4565, 12310, 792, 1, 21637, 14883, 26015, 6842, 14883, 1, 63261, 31185, 63261, 14883

Offset

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

With n = 9, 9 = 3 * 3. Since 9 - (3 + 3) = 3, and the partitions of 3 are {(3), (2, 1) (1, 1, 1)}, the partitions of 9 that include (3, 3) are {(3, 3, 3), (3, 3, 2, 1), (3, 3, 1, 1, 1)}, so a(9) = 3.

Maple

with(combinat):
a:= n-> numbpart(n-add(i[1]*i[2], i=ifactors(n)[2])):
seq(a(n), n=0..100);  # Alois P. Heinz, Feb 04 2014

Mathematica

a[n_] := PartitionsP[n-Sum[i[[1]]*i[[2]], {i, FactorInteger[n]}]]; Table[ a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Crossrefs

Cf. A236938, A237125.

Sequence in context: A214734 A120653 A323850 * A323748 A116155 A365991

Adjacent sequences: A236934 A236935 A236936 * A236938 A236939 A236940

Keyword

nonn,changed

Author

J. Stauduhar, Feb 01 2014

Extensions

More terms from Alois P. Heinz, Feb 04 2014

Status

approved