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

1,3

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)

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000961, A181063, A181064, A181121.

Includes A006093 as a subsequence.

Cf. A003418, A051451, A055874.

Sequence in context: A080389 A359755 A226038 * A338031 A091199 A093452

Adjacent sequences: A181059 A181060 A181061 * A181063 A181064 A181065

Keyword

easy,nonn

Author

Matthew Vandermast, Oct 07 2010

Extensions

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

Status

approved