cp's OEIS Frontend

A358011 Number of partitions of n into at most 6 distinct prime parts.

%I A358011 #16 May 14 2025 16:28:01
%S A358011 1,0,1,1,0,2,0,2,1,1,2,1,2,2,2,2,3,2,4,3,4,4,4,5,5,5,6,5,6,7,6,9,7,9,
%T A358011 9,9,11,11,11,13,12,14,15,15,17,16,18,19,20,21,23,22,25,26,27,30,29,
%U A358011 32,31,35,36,39,40,42,42,45,49,50,52,55,53,61,61,67,67,70,70,77,77,86,84
%N A358011 Number of partitions of n into at most 6 distinct prime parts.
%H A358011 Alois P. Heinz, <a href="/A358011/b358011.txt">Table of n, a(n) for n = 0..10000</a> (first 501 terms from Robert Israel)
%F A358011 a(n) = Sum_{k=0..6} A219180(n,k). - _Alois P. Heinz_, May 14 2025
%p A358011 P:= select(isprime,[2,seq(i,i=3..100,2)]):
%p A358011 G:= mul(1+t*x^p, p=P):
%p A358011 f:= proc(n) local i,S;
%p A358011    S:= coeff(G,x,n);
%p A358011    add(coeff(S,t,i),i=0..6)
%p A358011 end proc;
%p A358011 map(f, [$0..100]); # _Robert Israel_, May 14 2025
%Y A358011 Cf. A000040, A000586, A219180, A219200, A223893, A347550, A347588, A347610, A347743, A358009, A358010.
%K A358011 nonn,look
%O A358011 0,6
%A A358011 _Ilya Gutkovskiy_, Oct 24 2022