A093690 - OEIS

%I #4 Mar 30 2012 17:22:33

%S 37,41,43,59,97,107,127,137,149,157,163,167,181,211,241,269,307,311,

%T 373,383,419,421,433,457,467,479,487,491,499,547,563,569,571,577,601,

%U 617,619,643,653,659,677,709,727,739,787,797,811,821,859,863,883,911,929

%N Primes p that divide A007406(k), the numerator of the k-th generalized harmonic number H(k,2) = Sum 1/i^2 for i=1..k, for some k < (p-1)/2.

%C Because these primes are analogous to the irregular primes A000928 that divide the numerators of Bernoulli numbers, they might be called H2-irregular primes. Also see A092194. The density of these primes is about 0.4 - close to the density of irregular primes.

%t nn=1000; t=Numerator[HarmonicNumber[Range[nn], 2]]; lst = {}; Do[p=Prime[n]; i=1; While[i<(p-1)/2 && Mod[t[[i]], p]>0, i++ ]; If[i<(p-1)/2, AppendTo[lst, p]], {n, 3, PrimePi[nn]}]; lst

%Y Cf. A092194 (primes p that divide A001008(k) for some k < p-1), A093689 (least k such that prime(n) divides A007406(k)).

%K nonn

%O 1,1

%A _T. D. Noe_, Apr 09 2004