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

4,3

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Example

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.

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)<n do od; b(n, i, 0) end: seq(a(n), n=4..70);  # 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 *)

Crossrefs

Cf. A000607, A038499.

Sequence in context: A112213 A238957 A238970 * A330216 A241952 A236919

Adjacent sequences: A085752 A085753 A085754 * A085756 A085757 A085758

Keyword

nonn

Author

Vladeta Jovovic, Jul 21 2003

Status

approved