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

2,1

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

Formula

a(n) = A160995(n!).

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

Prog

(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

Crossrefs

Cf. A160995.

Sequence in context: A168038 A093995 A168280 * A014694 A065730 A246934

Adjacent sequences: A162561 A162562 A162563 * A162565 A162566 A162567

Keyword

nonn

Author

Leroy Quet, Jul 06 2009

Extensions

Extended by Emeric Deutsch, Jul 23 2009

Status

approved