A085755 Number of partitions of n into a prime number of prime parts.
1, 1, 2, 2, 2, 3, 4, 3, 4, 5, 6, 8, 8, 9, 9, 12, 12, 16, 16, 19, 19, 26, 24, 31, 29, 39, 35, 50, 44, 61, 55, 74, 67, 93, 80, 111, 99, 136, 119, 166, 145, 197, 179, 239, 213, 292, 255, 342, 310, 409, 365, 492, 436, 577, 524, 682, 614, 814, 724, 947, 865, 1113, 1007, 1314
Offset: 4
Keywords
Examples
a(20) = 12 because there are 12 partitions of 20 into a prime number of prime parts: 2+3+3+3+3+3+3 = 2+2+2+3+3+3+5 = 2+2+2+2+2+5+5 = 2+2+2+2+2+3+7 = 2+3+5+5+5 = 2+3+3+5+7 = 2+2+2+7+7 = 2+2+2+3+11 = 2+7+11 = 2+5+13 = 7+13 = 3+17.
Links
- Alois P. Heinz, Table of n, a(n) for n = 4..1000
Programs
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Maple
b:= proc(n, i, t) if n<0 then 0 elif n=0 then `if`(isprime(t), 1, 0) elif i=1 then `if`(irem(n,2)=0 and isprime(t +n/2), 1, 0) else b(n,i,t):= b(n -ithprime(i), i, t+1) +b(n, i-1, t) fi end: a:= proc(n) local i; for i while ithprime(i)
Alois P. Heinz, Apr 30 2009 -
Mathematica
Table[Length[Select[IntegerPartitions[n],PrimeQ[Length[#]]&&AllTrue[ #, PrimeQ]&]],{n,4,70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 18 2016 *)