A331849 Number of partitions of n into prime parts with some part repeated.

0, 0, 0, 0, 1, 0, 2, 1, 2, 3, 3, 5, 5, 7, 8, 10, 11, 15, 15, 20, 22, 26, 31, 35, 41, 47, 54, 62, 71, 80, 92, 102, 117, 131, 148, 166, 186, 208, 233, 259, 290, 322, 357, 398, 439, 488, 539, 595, 657, 723, 796, 877, 962, 1057, 1159, 1268, 1391, 1520, 1663, 1815, 1981

Offset

0,7

Links

Table of n, a(n) for n=0..60.

Index entries for sequences related to partitions

Formula

a(n) = A000607(n) - A000586(n).

Example

a(9) = 3 because we have [5, 2, 2], [3, 3, 3] and [3, 2, 2, 2].

Mathematica

Table[Count[IntegerPartitions[n], _?(AllTrue[#, PrimeQ]&&Length[Union[#]]<Length[#]&)], {n, 0, 60}] (* Harvey P. Dale, Feb 11 2025 *)

Crossrefs

Cf. A000586, A000607, A047967, A261982, A331848.

Sequence in context: A143472 A180235 A239493 * A015739 A015746 A109266

Adjacent sequences: A331846 A331847 A331848 * A331850 A331851 A331852

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Jan 29 2020

Status

approved