A181062 Prime powers minus 1.

0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 15, 16, 18, 22, 24, 26, 28, 30, 31, 36, 40, 42, 46, 48, 52, 58, 60, 63, 66, 70, 72, 78, 80, 82, 88, 96, 100, 102, 106, 108, 112, 120, 124, 126, 127, 130, 136, 138, 148, 150, 156, 162, 166, 168, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226

Offset: 1

Author

Matthew Vandermast, Oct 07 2010

Keywords

• easy
• nonn

Comments

If 0 is excluded, a(n) gives the possible lengths of the longest string of consecutive divisors of a positive integer: range of values of A055874.

a(n) is the largest number m such that A051451(n) = A003418(m).

From Jianing Song, Nov 01 2023: (Start)

Let q = A000961(n) for n > 1. Then:

- a(n) is the number of units in the finite field F_q.

- a(n) is the number of solutions to x*y = t for any t != 0 in F_q.

- If q is odd, then a(n) is also the number of solutions to x^2 - y^2 = t for any t != 0 in F_q. (End)

Examples

			Any integer that is divisible by 5 consecutive integers will be divisible by at least 6 consecutive integers. Hence 5 is not in the sequence.
		

Links

• Matthew House, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A181063, A181064, A181121.

Includes A006093 as a subsequence.

Cf. A003418, A051451, A055874.

Programs

Mathematica

Join[{0}, Select[Range@225, PrimePowerQ] - 1] (* Ivan Neretin, Aug 04 2016 *)

PARI

isA181062(n)=ispower(n++,,&n);isprime(n) \\ Charles R Greathouse IV, Jun 29 2011

PARI

isok(n) = (n==0) || isprimepower(n++); \\ Michel Marcus, Aug 05 2016

Formula

a(n) = A000961(n)-1.

Extensions

Entry revised by N. J. A. Sloane, Jan 06 2013