A232741 Numbers n for which the largest m such that (m-1)! divides n is a prime.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Author

Antti Karttunen, Dec 01 2013

Keywords

• nonn

Comments

Numbers n for which A055881(n) is one of the terms of A006093.

Equally: Numbers n for which {the number of the trailing zeros in their factorial base representation A007623(n)} + 2 is a prime.

The sequence can be described in the following manner: Sequence includes all multiples of 1! and 2! (odd and even numbers), except that it excludes from those the multiples of 3! (6), except that it includes the multiples of 4! (24), except that it excludes the multiples of 5! (120), except that it includes the multiples of 6! (720), except that it excludes the multiples of 7! (5040) (and also those of 8! and 9!, because here 8+1 = 9 is the first odd composite), except that it includes the multiples of 10!, but excludes the multiples of 11!, but includes the multiples of 12!, but excludes the multiples of 13! (and also of 14! and 15!, because 14-16 are all composites), but includes the multiples of 16!, and so on, ad infinitum.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8748

Crossrefs

Complement: A232742. Cf. A055926, A232744-A232745, A007623, A055881, A230403.