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A085755
Number of partitions of n into a prime number of prime parts.
12
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
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
Sequence in context: A112213 A238957 A238970 * A330216 A241952 A236919
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jul 21 2003
STATUS
approved