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%I #46 Nov 01 2023 10:02:05
%S 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,
%T 58,60,63,66,70,72,78,80,82,88,96,100,102,106,108,112,120,124,126,127,
%U 130,136,138,148,150,156,162,166,168,172,178,180,190,192,196,198,210,222,226
%N Prime powers minus 1.
%C 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.
%C a(n) is the largest number m such that A051451(n) = A003418(m).
%C From _Jianing Song_, Nov 01 2023: (Start)
%C Let q = A000961(n) for n > 1. Then:
%C - a(n) is the number of units in the finite field F_q.
%C - a(n) is the number of solutions to x*y = t for any t != 0 in F_q.
%C - 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)
%H Matthew House, <a href="/A181062/b181062.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000961(n)-1.
%e 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.
%t Select[Table[n, {n, 1, 350}], Length[FactorInteger[#]] == 1 &] - 1 (* _Vladimir Joseph Stephan Orlovsky_, Jun 28 2011 *)
%t Join[{0}, Select[Range@225, PrimePowerQ] - 1] (* _Ivan Neretin_, Aug 04 2016 *)
%o (PARI) isA181062(n)=ispower(n++,,&n);isprime(n) \\ _Charles R Greathouse IV_, Jun 29 2011
%o (PARI) isok(n) = (n==0) || isprimepower(n++); \\ _Michel Marcus_, Aug 05 2016
%Y Cf. A000961, A181063, A181064, A181121.
%Y Includes A006093 as a subsequence.
%Y Cf. A003418, A051451, A055874.
%K easy,nonn
%O 1,3
%A _Matthew Vandermast_, Oct 07 2010
%E Entry revised by _N. J. A. Sloane_, Jan 06 2013
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