A381251 a(n) is the number of ways to write prime(n) as a sum of distinct composites.

0, 0, 0, 0, 0, 1, 1, 3, 4, 10, 14, 27, 40, 52, 74, 133, 229, 276, 457, 626, 744, 1189, 1599, 2498, 4450, 5862, 6752, 8835, 10139, 13189, 32481, 41614, 60099, 67900, 122825, 138101, 195147, 274193, 342783, 477381, 661502, 736865, 1252245, 1390615, 1711496, 1897886

Offset: 1

Author

Felix Huber, Apr 19 2025

Keywords

• nonn

Comments

Subsequence of A204389.

All sums have an odd number of odd composite summands (A071904).

Examples

			a(8) = 3 because prime(8) = 19 can be written in 3 ways as a sum of distinct composites: 19 = 9 + 10 = 9 + 4 + 6 = 15 + 4.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A000040, A002808, A053872, A071904, A204389, A383037.

Programs

Maple

P:= [seq(ithprime(i),i=1..100)]:
C:= {$2..P[-1]} minus convert(P,set):
G:= mul(1+x^c,c=C):
seq(coeff(G,x,P[i]),i=1..100); # Robert Israel, Apr 22 2025

Formula

a(n) = A204389(A000040(n)). - R. J. Mathar, Apr 22 2025