

A181062


Prime powers minus 1.


9



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
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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



