

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
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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.
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



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) isok(n) = (n==0)  isprimepower(n++); \\ Michel Marcus, Aug 05 2016


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



