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

3,3

Links

Table of n, a(n) for n=3..58.

Formula

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

Example

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.

Sequence in context: A008756 A008755 A029006 * A350896 A008754 A029005

Adjacent sequences: A085753 A085754 A085755 * A085757 A085758 A085759

Keyword

nonn

Author

Vladeta Jovovic, Jul 21 2003

Status

approved