A162564 a(n) is the smallest positive integer neither coprime to n! nor a divisor of n!.

4, 4, 9, 9, 14, 22, 22, 22, 22, 26, 26, 34, 34, 34, 34, 38, 38, 46, 46, 46, 46, 58, 58, 58, 58, 58, 58, 62, 62, 74, 74, 74, 74, 74, 74, 82, 82, 82, 82, 86, 86, 94, 94, 94, 94, 106, 106, 106, 106, 106, 106, 118, 118, 118, 118, 118, 118, 122, 122, 134, 134, 134, 134, 134

Offset: 2

Author

Leroy Quet, Jul 06 2009

Keywords

• nonn

Comments

Alternately, smallest composite not dividing n!. For n > 5, twice the smallest prime greater than n. - Charles R Greathouse IV, Apr 04 2013

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A160995.

Programs

Maple

a := proc (n) local j: for j while gcd(j, factorial(n)) = 1 or `mod`(factorial(n), j) = 0 do end do: j end proc: seq(a(n), n = 2 .. 75); # Emeric Deutsch, Jul 23 2009

PARI

a(n)=my(N=n!,k=n);while(N%k++==0||isprime(k),);k \\ Charles R Greathouse IV, Apr 04 2013

PARI

a(n)=if(n>5,2*nextprime(n+1),(n\2+1)^2) \\ Charles R Greathouse IV, Apr 04 2013

Formula

a(n) = A160995(n!).

Extensions

Extended by Emeric Deutsch, Jul 23 2009