This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381251 #23 Apr 24 2025 13:23:57
%S A381251 0,0,0,0,0,1,1,3,4,10,14,27,40,52,74,133,229,276,457,626,744,1189,
%T A381251 1599,2498,4450,5862,6752,8835,10139,13189,32481,41614,60099,67900,
%U A381251 122825,138101,195147,274193,342783,477381,661502,736865,1252245,1390615,1711496,1897886
%N A381251 a(n) is the number of ways to write prime(n) as a sum of distinct composites.
%C A381251 Subsequence of A204389.
%C A381251 All sums have an odd number of odd composite summands (A071904).
%H A381251 Felix Huber, <a href="/A381251/b381251.txt">Table of n, a(n) for n = 1..4000</a>
%F A381251 a(n) = A204389(A000040(n)). - _R. J. Mathar_, Apr 22 2025
%e A381251 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.
%p A381251 P:= [seq(ithprime(i),i=1..100)]:
%p A381251 C:= {$2..P[-1]} minus convert(P,set):
%p A381251 G:= mul(1+x^c,c=C):
%p A381251 seq(coeff(G,x,P[i]),i=1..100); # _Robert Israel_, Apr 22 2025
%Y A381251 Cf. A000040, A002808, A053872, A071904, A204389, A383037.
%K A381251 nonn
%O A381251 1,8
%A A381251 _Felix Huber_, Apr 19 2025