A265112 a(n) = A023360(A000040(n)): number of compositions of prime(n) into prime parts.

1, 1, 3, 6, 20, 46, 232, 501, 2352, 24442, 53243, 550863, 2616338, 5701553, 27077005, 280237217, 2900328380, 6320545915, 65414893802, 310664269401, 677015556295, 7006815193063, 33276323565116, 344395408399372, 7767597342090622, 36889382062795742

Offset: 1

Author

Bob Selcoe, Dec 01 2015

Keywords

• nonn
• easy

Examples

			prime(4) = 7; a(4) = A023360(7) = 6 because there are 6 compositions of 7 into prime parts {2,3,5,7}: {7}, {5+2}, {3+2+2}, {2+5}, {2+3+2} and {2+2+3}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..768

Crossrefs

Cf. A000040 (prime numbers), A023360.

Programs

Maple

N:= 1000: # to get a(1) to a(A000720(N))
Primes:= select(isprime, [2,seq(i,i=3..N,2)]):
M:= nops(Primes);
F:= proc(x)
option remember;
local k;
add(procname(x-Primes[k]),k=1..numtheory:-pi(x));
end proc:
F(0):= 1:
seq(F(Primes[n]),n=1..M); # Robert Israel, Dec 02 2015

Mathematica

Needs["Combinatorica`"]; Table[Length@ Flatten[Permutations[#, {Length@ #}] & /@ Select[Combinatorica`Partitions@ Prime@ n, AllTrue[#, PrimeQ] &], 1], {n, 14}] (* Version 10, slow, or *)
lim = 101; t = Rest@ CoefficientList[Series[1/(1 - Sum[x^Prime[i], {i, 1, PrimePi@ lim}]), {x, 0, lim}], x]; t[[#]] &@ Prime@ Range@ PrimePi@ lim
(* Michael De Vlieger, Dec 01 2015, after David W. Wilson at A023360 *)