

A239412


Numbers n such that (n!k)/(nk) is prime for some k.


0



4, 6, 8, 16, 18, 92, 254, 258, 660, 1850, 2496, 2774, 2832, 7430, 28540, 32124
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(14) > 3000.
There is only one value of k that can work, and it is n/2. Thus, all members of the sequence are even.
Even numbers n such that 2*(n1)!1 is prime.
(Odd members of A076133) + 1.  Robert Israel, Aug 11 2016


LINKS

Table of n, a(n) for n=1..16.


EXAMPLE

(4!k)/(4k) is prime for some k (namely, k = 2). Thus, 4 is a member of this sequence.


MAPLE

select(t > isprime(2*(t1)!1), [seq(q, q=2..1000, 2)]); # Robert Israel, Aug 11 2016


MATHEMATICA

Select[Range[2, 10^3, 2], PrimeQ[2 (#  1)!  1] &] (* Michael De Vlieger, Aug 11 2016 *)


PROG

(PARI) a(n)=for(k=1, int(n/2), s=(n!k)/(nk); if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<1000, if(a(n), print1(n, ", ")); n+=1)


CROSSREFS

Cf. A076133.
Sequence in context: A095299 A079250 A055397 * A295006 A269833 A049421
Adjacent sequences: A239409 A239410 A239411 * A239413 A239414 A239415


KEYWORD

nonn,hard,more


AUTHOR

Derek Orr, May 26 2014


EXTENSIONS

Edited and a(14)a(16) added by Robert Israel, Aug 11 2016


STATUS

approved



