A180493 Numbers n such that prime(n)! is divisible by A180491(prime(n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 35, 38, 39, 40, 53

Offset: 1

Author

Carl R. White, Sep 08 2010

Keywords

• hard
• more
• nonn

Comments

Also numbers n such that prime(n)! is divisible by A180492(n).

Is this sequence finite?

From Robert G. Wilson v, Sep 09 2010: (Start)

Checked to 10000 for more terms.

Conjecture: This sequence is finite and all its terms are present. (End)

Crossrefs

Cf. A034386, A000142, A004125, A180491, A180492.

Programs

Mathematica

f[n_] := Times @@ Mod[n, Range[2, n - 1]]; k = 1; lst = {}; While[k < 10001, If[ Divisible[ Prime@k!, f@Prime@k], AppendTo[lst, k]; Print@k]; k++ ]; lst (* Robert G. Wilson v, Sep 09 2010 *)