OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..768
EXAMPLE
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}.
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bob Selcoe, Dec 01 2015
STATUS
approved