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A181062 Prime powers minus 1. 13
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 (list; graph; refs; listen; history; text; internal format)
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
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
Includes A006093 as a subsequence.
Sequence in context: A080389 A359755 A226038 * A338031 A091199 A093452
KEYWORD
easy,nonn
AUTHOR
Matthew Vandermast, Oct 07 2010
EXTENSIONS
Entry revised by N. J. A. Sloane, Jan 06 2013
STATUS
approved

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Last modified June 14 07:34 EDT 2024. Contains 373393 sequences. (Running on oeis4.)