A043298 Numbers n such that B(6*n) has denominator 42 where B(2k) are the Bernoulli numbers.

1, 19, 31, 43, 59, 67, 71, 79, 97, 109, 127, 139, 149, 157, 163, 167, 193, 197, 199, 211, 223, 227, 229, 269, 307, 317, 337, 349, 353, 361, 379, 383, 389, 401, 409, 421, 433, 439, 449, 457, 463, 479, 487, 499, 521, 523, 541, 547, 563, 569, 571, 587, 589, 599

Offset: 1

Author

Benoit Cloitre, Mar 24 2002

Keywords

• easy
• nonn

Comments

Except for 1 and 361=19^2 terms listed are primes.

Most a(n) are primes p such that 2p+1 is composite A053176. Nonprime a(n) (except a(1) = 1) are the powers or the products of primes from a(n). For example, 361 = 19^2, 589 = 19*31, 961 = 31^2, 1333 = 31*43, 1849 = 43^2, 2071 = 19*109, 2077 = 31*67, 2201 = 31*71, 2449 = 31*79, 2537 = 43*59, 2641 = 19*139, 2881 = 43*67, 2983 = 19*157, 3053 = 43*71, 3173 = 19*167, ..., 6859 = 19^3. - Alexander Adamchuk, Jul 28 2006

Links

• Enrique Pérez Herrero, Table of n, a(n) for n=1..50000

Crossrefs

Cf. A051225, A053176.

Programs

Mathematica

Do[s=1+Divisors[n]; s1=Flatten[Position[PrimeQ[s], True]]; s2=Part[s, s1]; If[Equal[s2, {2, 3, 7}], Print[n/6]], {n, 1, 10000}] (* Alexander Adamchuk, Jul 28 2006 *)
Select[Range[600],Denominator[BernoulliB[6#]]==42&] (* Harvey P. Dale, Jan 09 2024 *)

Extensions

Corrected and extended by Ralf Stephan, Oct 21 2002

More terms from Alexander Adamchuk, Jul 28 2006