A112772 Semiprimes of the form 6n+2.

14, 26, 38, 62, 74, 86, 122, 134, 146, 158, 194, 206, 218, 254, 278, 302, 314, 326, 362, 386, 398, 422, 446, 458, 482, 542, 554, 566, 614, 626, 662, 674, 698, 734, 746, 758, 794, 818, 842, 866, 878, 914, 926, 974, 998, 1046, 1082, 1094, 1142, 1154, 1202, 1214

Offset: 1

Author

Jonathan Vos Post and Ray Chandler, Oct 15 2005

Keywords

• easy
• nonn

Comments

{6} + A112772 + A112774 = A100484 = 2*A000040.

Rado showed that for a given Bernoulli number B_n there exist infinitely many Bernoulli numbers B_m having the same denominator. As a special case, if n = 2p where p is an odd prime p == 1 (mod 3), then the denominator of the Bernoulli number B_n equals 6. - Bernd C. Kellner, Mar 21 2018

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• R. Rado, A note on the Bernoullian numbers, J. London Math. Soc. 9 (1934) 88-90.

Crossrefs

Subsequence of A051222. - Bernd C. Kellner, Mar 21 2018

Cf. A027642.

Programs

Magma

IsSemiprime:= func; [s: n in [0..210] | IsSemiprime(s) where s is 6*n + 2]; // Vincenzo Librandi, Sep 22 2012

Mathematica

Select[6Range[0,300]+2,PrimeOmega[#]==2&] (* Harvey P. Dale, Oct 04 2011 *)

PARI

2*select(n->n%3==1,primes(100)) \\ Charles R Greathouse IV, Sep 22 2012

Formula

a(n) = 2 * A002476(n) = 6 * A024892(n) + 2.

denominator(Bernoulli(a(n))) = 6. - Bernd C. Kellner, Mar 21 2018