A347578 -id:A347578 - cp's OEIS frontend

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

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

A347610 Number of partitions of n into at most 6 prime parts.

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 9, 11, 12, 14, 15, 17, 18, 20, 23, 24, 27, 28, 32, 33, 37, 38, 43, 44, 48, 51, 55, 55, 63, 62, 70, 71, 77, 78, 89, 87, 97, 96, 108, 105, 121, 114, 133, 127, 144, 139, 161, 149, 174, 165, 189, 177, 208, 188, 226, 206

Offset: 0

Ilya Gutkovskiy, Sep 08 2021

nonn

Cf. A000040, A000607, A071335, A117278, A259196, A347552, A347578, A347609.

a(n) = Sum_{k=1..6} 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

A347623 Number of partitions of n into at most 4 prime parts (counting 1 as a prime).

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 9, 10, 10, 12, 11, 14, 13, 15, 14, 18, 15, 20, 17, 22, 18, 25, 19, 26, 20, 26, 21, 30, 23, 33, 24, 35, 26, 38, 27, 40, 28, 41, 31, 48, 32, 50, 34, 53, 36, 58, 37, 60, 39, 61, 40, 67, 40, 68, 41, 72, 45, 79, 47, 82, 49

Offset: 0

Ilya Gutkovskiy, Sep 09 2021

nonn

Cf. A008578, A034891, A218007, A341947, A347578, A347622, A347624, A347625.

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.

cp's OEIS Frontend

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

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A347610 Number of partitions of n into at most 6 prime parts.

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

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A347623 Number of partitions of n into at most 4 prime parts (counting 1 as a prime).

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

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