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A181062 Prime powers minus 1. 10
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) = largest number m such that A051451(n) = A003418(m).

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

Select[Table[n, {n, 1, 350}], Length[FactorInteger[#]] == 1 &] - 1 (* Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)

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: A221178 A080389 A226038 * A091199 A093452 A082103

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

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Last modified March 31 19:16 EDT 2020. Contains 333151 sequences. (Running on oeis4.)