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

Author

Ilya Gutkovskiy, Jan 29 2020

Keywords

• nonn

Examples

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

Links

• Index entries for sequences related to partitions

Crossrefs

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

Programs

Mathematica

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

Formula

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