A358011 Number of partitions of n into at most 6 distinct prime parts.

1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 6, 5, 6, 7, 6, 9, 7, 9, 9, 9, 11, 11, 11, 13, 12, 14, 15, 15, 17, 16, 18, 19, 20, 21, 23, 22, 25, 26, 27, 30, 29, 32, 31, 35, 36, 39, 40, 42, 42, 45, 49, 50, 52, 55, 53, 61, 61, 67, 67, 70, 70, 77, 77, 86, 84

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 501 terms from Robert Israel)

Formula

a(n) = Sum_{k=0..6} A219180(n,k). - Alois P. Heinz, May 14 2025

Maple

P:= select(isprime, [2, seq(i, i=3..100, 2)]):
G:= mul(1+t*x^p, p=P):
f:= proc(n) local i, S;
   S:= coeff(G, x, n);
   add(coeff(S, t, i), i=0..6)
end proc;
map(f, [$0..100]); # Robert Israel, May 14 2025

Crossrefs

Cf. A000040, A000586, A219180, A219200, A223893, A347550, A347588, A347610, A347743, A358009, A358010.

Sequence in context: A358009 A358010 A112022 * A000586 A029399 A302172

Adjacent sequences: A358008 A358009 A358010 * A358012 A358013 A358014

Keyword

nonn,look

Author

Ilya Gutkovskiy, Oct 24 2022

Status

approved