cp's OEIS Frontend

A181676 Number of ways of writing n = m + f! with m a semiprime and f > 0.

%I A181676 #9 Sep 20 2024 23:55:00
%S A181676 0,0,0,0,1,1,1,1,0,2,2,2,0,0,2,3,1,0,0,1,1,1,2,1,0,1,3,3,0,1,1,1,1,2,
%T A181676 2,2,1,1,3,3,2,0,0,1,2,1,1,1,1,2,1,2,1,0,1,1,3,2,3,1,1,1,3,2,0,1,1,1,
%U A181676 0,2,2,0,1,0,3,1,0,1,2,1,1,1,2,1,0,2,2,3,2,0,1,2,3,1,2,2,2,1,1,1,2,0,0,0,0
%N A181676 Number of ways of writing n = m + f! with m a semiprime and f > 0.
%C A181676 Number of partitions of n into a semiprime and a factorial.
%H A181676 Robert Israel, <a href="/A181676/b181676.txt">Table of n, a(n) for n = 1..10000</a>
%e A181676 a(16)=3 because 16 = 2*5 + 3! = 2*7 + 2! = 3*5 + 1!.
%p A181676 N:= 200: # for a(1) .. a(N)
%p A181676 R:= Vector(N):
%p A181676 S:= select(t -> numtheory:-bigomega(t)=2, [$1..N]):
%p A181676 F:= 1: v:= 1:
%p A181676 for i from 2 do v:= v*i; if v > N then break fi; F:= F,v od:
%p A181676 F:= [F]:
%p A181676 for s in S do
%p A181676   for f in F do
%p A181676     v:= s+f;
%p A181676      if v > N then break fi;
%p A181676      R[v]:= R[v]+1
%p A181676 od od:
%p A181676 convert(R,list); # _Robert Israel_, Sep 20 2024
%Y A181676 Cf. A000142, A001358, A175940.
%K A181676 nonn
%O A181676 1,10
%A A181676 _Juri-Stepan Gerasimov_, Nov 04 2010