A269665 For n>=0, let A_n be the set of natural numbers k such that (k^n + 1) | k!. If A is nonempty, then a(n) is the least element of A_n; otherwise a(n) = 0.

2, 5, 18, 17, 1600, 984, 2888, 460747, 99271723, 792174, 32917926

Offset

0,1

Comments

a(n) is the smallest k such that (k^n + 1) | k! if it exists, otherwise a(n) = 0.

Links

Table of n, a(n) for n=0..10.

Example

For n=2, a(2) is equal to 18 because k=18 is the least natural number k such that (k^2+1)|k! (see A120416).

Mathematica

For[k = 0, k < 11, k++, x = 0; r = 0; n = 1; While[x != 1, If[Mod[n!, n^k + 1] != 0, x = 0, x = 1; r = n]; n++]; Print[r]]
Table[SelectFirst[Range[10^4], Divisible[#!, #^n + 1] &], {n, 0, 6}] (* Michael De Vlieger, Mar 04 2016, Version 10 *)

Prog

(PARI) a(n) = {my(k = 1); while (k! % (k^n+1), k++); k; } \\ Michel Marcus, Mar 03 2016

Crossrefs

Cf. A118742, A120416, A270441.

Sequence in context: A226069 A258429 A117839 * A080689 A026321 A288994

Adjacent sequences: A269662 A269663 A269664 * A269666 A269667 A269668

Keyword

nonn,more

Author

José Hernández, Mar 02 2016

Extensions

a(7)-a(9) from Hiroaki Yamanouchi, Apr 04 2016

a(10) from Giovanni Resta, Apr 20 2016

Status

approved