A347550 -id:A347550 - cp's OEIS frontend

A358010 Number of partitions of n into at most 5 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, 13, 15, 15, 17, 15, 18, 17, 20, 20, 23, 20, 25, 22, 27, 28, 28, 27, 30, 29, 36, 34, 38, 36, 41, 35, 48, 41, 48, 44, 50, 46, 58, 53, 61, 54, 64, 55, 72, 66, 74

Offset: 0

Ilya Gutkovskiy, Oct 24 2022

nonn

Cf. A000040, A000586, A219180, A219199, A223893, A347550, A347587, A347609, A347742, A358009, A358011.

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Oct 24 2022

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

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

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

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

A358009 Number of partitions of n into at most 4 distinct prime parts.

Original entry on oeis.org

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, 5, 7, 5, 9, 7, 9, 7, 9, 9, 11, 9, 12, 8, 13, 11, 14, 13, 13, 12, 16, 14, 18, 17, 16, 17, 20, 17, 23, 19, 21, 19, 24, 23, 28, 24, 26, 25, 26, 30, 30, 29, 29, 29, 32, 36, 37, 36, 32, 38, 35, 43, 41, 43, 20

Offset: 0

Ilya Gutkovskiy, Oct 24 2022

nonn

Cf. A000040, A000586, A219180, A219198, A223893, A347550, A347578, A347586, A347741, A358010, A358011.

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A358010 Number of partitions of n into at most 5 distinct prime parts.

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

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A358009 Number of partitions of n into at most 4 distinct prime parts.

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