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

1,1

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

Formula

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

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 *)

Crossrefs

Cf. A000146, A027642.

Sequence in context: A358468 A173924 A307392 * A257246 A056206 A257245

Adjacent sequences: A046883 A046884 A046885 * A046887 A046888 A046889

Keyword

nonn

Author

Wouter Meeussen, Jan 23 2001

Status

approved