A210684 -id:A210684 - cp's OEIS frontend

A043297 Primes p such that B(4*p) has denominator 30 where B(2n) are the Bernoulli numbers.

2, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, 211, 223, 227, 229, 241, 257, 263, 269, 271, 283, 311, 313, 317, 331, 337, 347, 349, 353, 367, 379, 383, 389, 397, 401, 421, 439, 449, 457, 461, 463, 467, 479, 503, 521

Offset: 1

Benoit Cloitre, Mar 24 2002

Complement of A087634, primes p such that phi(k) = 4p has a solution, where phi is Euler's totient function.
The sequences a(n), A005384 and A023212 form a partition of the set of primes > 3: Using von Staudt-Clausen formula the divisors of 4p increased by 1 are {2,3,5,p+1,2p+1,4p+1}, p+1 is clearly an even number, and if 2p+1 and 4p+1 are not prime, then denom(B(4p))=30. - Enrique Pérez Herrero, Aug 15 2011
Also 2 with the primes p such that both 2*p+1 and 4*p+1 are composite: A210684. For these numbers k > 2 the equation: phi(n)=k*tau(n), where phi is A000010 and tau is A000005, has no solutions: A112954(a(n))=0. - Enrique Pérez Herrero, May 12 2012

E. Pérez Herrero, Table of n, a(n) for n=1..30000
Wikipedia, Von Staudt-Clausen theorem

Cf. A051225, A053176, A087634.
Cf. A005384, A023212.
Cf. A210684.

Select[Prime[Range[100]], Denominator[BernoulliB[4# ]]==30&] (* T. D. Noe, Feb 19 2004 *)
Select[Prime[Range[100]],!PrimeQ[4#+1]&&!PrimeQ[2#+1]||(#==2)&] (* Enrique Pérez Herrero, Aug 16 2011 *)

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A043297 Primes p such that B(4*p) has denominator 30 where B(2n) are the Bernoulli numbers.

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