A014076 Odd nonprimes.

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

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

Warut Roonguthai

Status

approved