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

%I A046886 #15 Aug 07 2022 08:14:32
%S A046886 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,
%T A046886 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,
%U A046886 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
%N A046886 Number of divisors d of 2n satisfying (d+1) = prime or number of prime factors of the denominator of the even Bernoulli numbers.
%C A046886 From von Staudt-Clausen theorem.
%D A046886 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
%D A046886 Hans Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
%H A046886 Amiram Eldar, <a href="/A046886/b046886.txt">Table of n, a(n) for n = 1..10000</a>
%F A046886 a(n) = A067513(2n). - _R. J. Mathar_, Aug 07 2022
%p A046886 A046886 := proc(n)
%p A046886     A067513(2*n) ;
%p A046886 end proc:
%p A046886 seq(A046886(n),n=1..100) ; # _R. J. Mathar_, Aug 07 2022
%t A046886 Length[ Select[ Divisors[ 2n ], PrimeQ[ #+1 ]& ] ] or Length[ FactorInteger[ Denominator@BernoulliB[ 2k ] ] ]
%t A046886 Table[Count[Divisors[2n],_?(PrimeQ[#+1]&)],{n,110}] (* or *) PrimeOmega/@ Denominator[BernoulliB[2*Range[110]]] (* _Harvey P. Dale_, Mar 19 2015 *)
%Y A046886 Cf. A000146, A027642.
%K A046886 nonn
%O A046886 1,1
%A A046886 _Wouter Meeussen_, Jan 23 2001