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%I #16 Jan 18 2014 16:32:31
%S -1,1,1,1,1,9,1,1,15,1,1,21,1,25,27,1,1,33,35,1,39,1,1,45,1,49,51,1,
%T 55,57,1,1,63,65,1,69,1,1,75,77,1,81,1,85,87,1,91,93,95,1,99,1,1,105,
%U 1,1,111,1,115,117,119,121,123
%N a(n) = 2*n - numerator((2*n-1)^2/(2*(2*n)!)).
%C Odd composite numbers with placeholders for primes between them.
%F a(n) = 2*n - A128059(n)
%F a(n) = (A217983(n-1) * (2*n-1))/A160479(n) for n >= 3. [_Johannes W. Meijer_, Oct 25 2012]
%F a(0) = -1, a(n) = GCD(2n-1, (2n-2)!), n > 0. - _Wesley Ivan Hurt_, Jan 05 2014
%p A128060 := proc(n): 2*n - numer((2*n-1)^2/(2*(2*n)!)) end: seq(A128060(n), n=0..62);
%p # End program 1 [_Johannes W. Meijer_, Oct 25 2012]
%p A128060 := proc(n) local n1: n1:=2*n-1: if type(n1, prime) then A128060(n) := 1 else A128060(n) := n1 fi: end: seq(A128060(n), n=0..62);
%p # End program 2 [_Johannes W. Meijer_, Oct 25 2012]
%t Table[2n - Numerator[(2n - 1)^2/(2(2n)!)], {n, 0, 74}] (* _Alonso del Arte_, Jan 05 2014 *)
%K easy,sign
%O 0,6
%A _Paul Barry_, Feb 13 2007
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