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.
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
KEYWORD
easy,nonn
AUTHOR
Matthew Vandermast, Oct 07 2010
EXTENSIONS
Entry revised by N. J. A. Sloane, Jan 06 2013
STATUS
approved