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A085755 Number of partitions of n into a prime number of prime parts. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

Equals 2 * A005773, n>0.

Sequence in context: A112213 A238957 A238970 * A241952 A236919 A138304

Adjacent sequences:  A085752 A085753 A085754 * A085756 A085757 A085758

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jul 21 2003

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.