A085756 Number of partitions into a prime number of distinct parts.

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 20, 22, 26, 30, 35, 40, 47, 53, 62, 71, 82, 93, 108, 123, 141, 161, 184, 209, 239, 271, 309, 350, 397, 449, 509, 575, 649, 732, 825, 928, 1044, 1172, 1315, 1474, 1650, 1845, 2061, 2300, 2563, 2854, 3174, 3526, 3912, 4337

Offset: 3

Author

Vladeta Jovovic, Jul 21 2003

Keywords

• nonn

Examples

			a(15)=20 because there are 20 partitions of 15 into a prime number of distinct parts: 1+2+3+4+5=4+5+6=3+5+7=2+6+7=3+4+8=2+5+8=1+6+8=7+8=2+4+9=1+5+9=6+9=2+3+10=
1+4+10=5+10=1+3+11=4+11=1+2+12=3+12=2+13=1+14.
		

Crossrefs

Cf. A038499.

Formula

a(n) = A004526(n-1) +A001399(n-6) +A001401(n-15) +A008636(n-28) + .... - R. J. Mathar, Feb 13 2019