

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
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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



