A298604 Number of partitions of n into distinct odd prime parts (including 1).

1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 5, 5, 6, 6, 7, 7, 8, 9, 8, 9, 10, 11, 12, 11, 12, 14, 14, 15, 16, 17, 17, 17, 20, 22, 21, 22, 24, 25, 27, 28, 30, 31, 31, 33, 36, 39, 40, 40, 42, 46, 47, 49, 53, 54, 55, 58, 63, 67, 68, 70, 73, 77, 81, 84

Offset

0,9

Links

Table of n, a(n) for n=0..78.

Index entries for related partition-counting sequences

Formula

G.f.: (1 + x)*Product_{k>=2} (1 + x^prime(k)).

Example

a(16) = 3 because we have [13, 3], [11, 5] and [7, 5, 3, 1].

Mathematica

nmax = 78; CoefficientList[Series[(1 + x) Product[(1 + x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000586, A006005, A008578, A024939, A036497, A298603.

Sequence in context: A123584 A291983 A112689 * A190353 A331904 A025829

Adjacent sequences: A298601 A298602 A298603 * A298605 A298606 A298607

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2018

Status

approved