A085756 - OEIS

%I #6 Feb 13 2019 09:00:18

%S 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,

%T 123,141,161,184,209,239,271,309,350,397,449,509,575,649,732,825,928,

%U 1044,1172,1315,1474,1650,1845,2061,2300,2563,2854,3174,3526,3912,4337

%N Number of partitions into a prime number of distinct parts.

%F a(n) = A004526(n-1) +A001399(n-6) +A001401(n-15) +A008636(n-28) + .... - _R. J. Mathar_, Feb 13 2019

%e 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=

%e 1+4+10=5+10=1+3+11=4+11=1+2+12=3+12=2+13=1+14.

%Y Cf. A038499.

%K nonn

%O 3,3

%A _Vladeta Jovovic_, Jul 21 2003