login
A175940
Number of ways of writing n=p+f with p a prime and f a factorial.
5
0, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 1, 1, 3, 1, 1, 0, 2, 1, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 3, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 1, 3, 1, 1
OFFSET
1,4
COMMENTS
Number of partitions of n into the sum of a prime number and a factorial number. Number of decompositions of n into an unordered sum of a prime number and a factorial number.
LINKS
EXAMPLE
a(29)=2 because 29 has two prime + factorial representations, 5+4! and 23+3!.
MAPLE
a:= proc(n) local t, k;
t:= 0;
for k while k! < n do
if isprime(n-k!) then t:= t+1 fi
od;
t
end proc:
seq(a(n), n=1..100); # Robert Israel, Oct 13 2014
MATHEMATICA
a[n_] := Module[{t = 0, k}, For[k = 1, k! < n, k++, If[PrimeQ[n - k!] , t++]]; t];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 02 2023, after Robert Israel *)
PROG
(PARI)
a(n) = c=0; for(i=1, n, if(isprime(n-i!), c++)); c
vector(100, n, a(n)) \\ Derek Orr, Oct 13 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and entries checked by D. S. McNeil, Nov 26 2010
STATUS
approved