A347610 -id:A347610 - cp's OEIS frontend

A347578 Number of partitions of n into at most 4 prime parts.

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 9, 11, 11, 13, 11, 15, 12, 16, 15, 16, 15, 18, 16, 20, 17, 23, 18, 24, 20, 26, 22, 26, 23, 31, 23, 33, 26, 35, 26, 39, 27, 41, 32, 41, 31, 46, 31, 48, 34, 51, 34, 54, 36, 58, 40, 58, 42, 64, 41

Offset: 0

Ilya Gutkovskiy, Sep 08 2021

nonn

Cf. A000040, A000607, A071335, A117278, A259194, A347552, A347609, A347610.

a(n) = Sum_{k=1..4} A117278(n,k) for n >= 2. - Alois P. Heinz, Sep 08 2021

A347609 Number of partitions of n into at most 5 prime parts.

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 8, 8, 9, 10, 11, 11, 14, 14, 15, 17, 18, 19, 21, 22, 23, 25, 27, 27, 32, 29, 34, 33, 37, 37, 42, 39, 47, 44, 51, 47, 58, 50, 61, 57, 67, 61, 73, 65, 80, 71, 86, 75, 95, 79, 101, 86, 107, 92, 115, 95, 125, 103, 132, 108

Offset: 0

Ilya Gutkovskiy, Sep 08 2021

nonn

Cf. A000040, A000607, A071335, A117278, A259195, A347552, A347578, A347610.

a(n) = Sum_{k=1..5} A117278(n,k) for n >= 2. - Alois P. Heinz, Sep 08 2021

A347552 Number of partitions of n into at most 2 prime parts.

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 1, 3, 0, 2, 1, 3, 2, 2, 1, 4, 0, 4, 1, 2, 1, 3, 1, 4, 2, 3, 1, 4, 1, 5, 1, 4, 0, 3, 1, 5, 1, 3, 0, 4, 1, 6, 2, 3, 1, 5, 0, 6, 1, 2, 1, 5, 1, 6, 2, 5, 1, 5, 0, 7, 1, 4, 1, 5, 1, 8, 1, 5

Offset: 0

Ilya Gutkovskiy, Sep 08 2021

nonn

Cf. A000040, A000607, A061358, A071335, A117278, A347578, A347609, A347610.

a(n) = Sum_{k=1..2} A117278(n,k) for n >= 2. - Alois P. Heinz, Sep 08 2021

A347625 Number of partitions of n into at most 6 prime parts (counting 1 as a prime).

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 8, 10, 12, 14, 17, 19, 22, 24, 27, 29, 33, 35, 40, 41, 47, 48, 56, 56, 65, 64, 75, 73, 85, 82, 96, 91, 106, 101, 119, 111, 133, 123, 147, 136, 162, 149, 180, 162, 196, 177, 217, 194, 238, 209, 259, 228, 282, 247, 307, 263, 330, 284, 357, 303, 383

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A008578, A034891, A218007, A341949, A347610, A347622, A347623, A347624.

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

cp's OEIS Frontend

A347578 Number of partitions of n into at most 4 prime parts.

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A347609 Number of partitions of n into at most 5 prime parts.

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A347552 Number of partitions of n into at most 2 prime parts.

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A347625 Number of partitions of n into at most 6 prime parts (counting 1 as a prime).

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

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