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

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, 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, 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

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 04 2010

Keywords

• nonn

Comments

Number of partitions of n into a semiprime and a factorial.

Examples

			a(16)=3 because 16 = 2*5 + 3! = 2*7 + 2! = 3*5 + 1!.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000142, A001358, A175940.

Programs

Maple

N:= 200: # for a(1) .. a(N)
R:= Vector(N):
S:= select(t -> numtheory:-bigomega(t)=2, [$1..N]):
F:= 1: v:= 1:
for i from 2 do v:= v*i; if v > N then break fi; F:= F,v od:
F:= [F]:
for s in S do
  for f in F do
    v:= s+f;
     if v > N then break fi;
     R[v]:= R[v]+1
od od:
convert(R,list); # Robert Israel, Sep 20 2024