OFFSET
1,1
COMMENTS
k <= n for all n so k can only be a finite set of numbers.
Only k dividing n need be considered.
By Wilson's theorem, all primes > 3 are in the sequence. - Robert Israel, Jul 31 2014
LINKS
Jens Kruse Andersen, Table of n, a(n) for n = 1..1000
EXAMPLE
(1!+5)/1 = 6 is not prime.
(2!+5)/2 = 7/2 is not prime.
(3!+5)/3 = 11/3 is not prime.
(4!+5)/4 = 29/4 is not prime.
(5!+5)/5 = 25 is not prime.
For any k > 5, (k!+5)/k = (k-1)! + 5/k will always be a fraction and thus, never prime. So 5 is a member of this sequence.
MAPLE
filter:= proc(n) local k;
for k in numtheory:-divisors(n) do
if isprime((k!+n)/k) then return false fi
od:
true
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 31 2014
MATHEMATICA
filterQ[n_] := AllTrue[Divisors[n], !PrimeQ[(#! + n)/#]&];
Select[Range[200], filterQ] (* Jean-François Alcover, Jul 27 2020 *)
PROG
(PARI)
a(n)=for(k=1, n, s=(k!+n)/k; if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<200, if(!a(n), print1(n, ", ")); n++)
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Jul 31 2014
STATUS
approved