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 A014076 Odd nonprimes. 69
 1, 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 121, 123, 125, 129, 133, 135, 141, 143, 145, 147, 153, 155, 159, 161, 165, 169, 171, 175, 177, 183, 185, 187, 189, 195, 201, 203, 205, 207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Same as A071904 except for the initial term 1 (which is not composite). Numbers n such that product of first n odd numbers divided by sum of the first n odd numbers is an integer : 1*3*5*...*(2*n - 1) / (1 + 3 + 5 + ... + (2*n - 1)) = c. - Ctibor O. Zizka, Jun 26 2010 Conjecture: There exist infinitely many pairs [a(n), a(n)+6] such that a(n)/3 and (a(n)+6)/3 are twin primes. - Eric Desbiaux, Sep 25 2014. Odd numbers 2*n + 1 such that (2*n)!/(2*n + 1) is an integer. Odd terms of A056653. - Peter Bala, Jan 24 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA A000035(a(n))*(1 - A010051(a(n)) = 1. - Reinhard Zumkeller, Sep 30 2011 a(n) ~ 2n. - Charles R Greathouse IV, Jul 02 2013 (a(n+2)-1)/2 - pi(a(n+2)-1) = n. - Anthony Browne, May 25 2016. Proof from Robert Israel: This follows by induction on n. If f(n) = (a(n+2)-1)/2 - pi(a(n+2)-1), one can show f(n+1) - f(n) = 1 (there are three cases to consider, depending on primeness of a(n+2) + 2 and a(n+2) + 4). Union of A091113 and A091236. - R. J. Mathar, Oct 02 2018 MAPLE remove(isprime, [seq(i, i=1..1000, 2)]); # Robert Israel, May 25 2016 for n from 0 to 120 do if irem(factorial(2*n), 2*n+1) = 0 then print(2*n+1) end if; end do: # Peter Bala, Jan 24 2017 MATHEMATICA Select[Range@210, !PrimeQ@ # && OddQ@ # &] (* Robert G. Wilson v, Sep 22 2008 *) Select[Range[1, 199, 2], PrimeOmega[#] != 1 &] (* Alonso del Arte, Nov 19 2012 *) PROG (Haskell) a014076 n = a014076_list !! (n-1) a014076_list = filter ((== 0) . a010051) a005408_list -- Reinhard Zumkeller, Sep 30 2011 (PARI) is(n)=n%2 && !isprime(n) \\ Charles R Greathouse IV, Nov 24 2012 CROSSREFS Cf. A002808, A005408; first differences: A067970, A196274; A047846. Cf. A056653. Sequence in context: A270574 A071904 A326586 * A067800 A155474 A100819 Adjacent sequences:  A014073 A014074 A014075 * A014077 A014078 A014079 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)