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 A181062 Prime powers minus 1. 10

%I

%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) = largest number m such that A051451(n) = A003418(m).

%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. 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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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)