A093689 -id:A093689 - cp's OEIS frontend

A093690 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.

37, 41, 43, 59, 97, 107, 127, 137, 149, 157, 163, 167, 181, 211, 241, 269, 307, 311, 373, 383, 419, 421, 433, 457, 467, 479, 487, 491, 499, 547, 563, 569, 571, 577, 601, 617, 619, 643, 653, 659, 677, 709, 727, 739, 787, 797, 811, 821, 859, 863, 883, 911, 929

Offset: 1

T. D. Noe, Apr 09 2004

nonn

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.

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

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

cp's OEIS Frontend

A093690 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.

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