A046886 Number of divisors d of 2n satisfying (d+1) = prime or number of prime factors of the denominator of the even Bernoulli numbers.

2, 3, 3, 3, 3, 5, 2, 4, 4, 4, 3, 5, 2, 4, 5, 4, 2, 7, 2, 5, 4, 4, 3, 6, 3, 4, 4, 4, 3, 8, 2, 4, 5, 3, 4, 8, 2, 3, 4, 6, 3, 7, 2, 5, 6, 4, 2, 7, 2, 5, 4, 4, 3, 8, 4, 6, 3, 4, 2, 9, 2, 3, 6, 4, 4, 7, 2, 4, 5, 6, 2, 9, 2, 4, 6, 3, 3, 8, 2, 6, 5, 4, 3, 7, 3, 4, 4, 6, 3, 11, 2, 4, 3, 3, 4, 8, 2, 5, 7, 6, 2, 6, 2, 5

Offset: 1

Author

Wouter Meeussen, Jan 23 2001

Keywords

• nonn

Comments

From von Staudt-Clausen theorem.

References

• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
• Hans Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000146, A027642.

Programs

Maple

A046886 := proc(n)
    A067513(2*n) ;
end proc:
seq(A046886(n),n=1..100) ; # R. J. Mathar, Aug 07 2022

Mathematica

Length[ Select[ Divisors[ 2n ], PrimeQ[ #+1 ]& ] ] or Length[ FactorInteger[ Denominator@BernoulliB[ 2k ] ] ]
Table[Count[Divisors[2n],?(PrimeQ[#+1]&)],{n,110}] (* or *) PrimeOmega/@ Denominator[BernoulliB[2*Range[110]]] (* _Harvey P. Dale, Mar 19 2015 *)

Formula

a(n) = A067513(2n). - R. J. Mathar, Aug 07 2022