A092195 Primes p that do not divide A001008(k), the numerator of the k-th harmonic number H(k), for any k < p-1.

3, 5, 7, 13, 17, 19, 23, 31, 41, 47, 59, 67, 71, 73, 79, 83, 89, 101, 103, 107, 113, 127, 131, 139, 149, 151, 157, 163, 167, 179, 181, 191, 193, 197, 211, 223, 229, 233, 239, 241, 251, 263, 277, 281, 283, 293, 307, 311, 317, 331, 337, 349, 359, 367, 373, 383

Offset: 1

Author

T. D. Noe, Feb 24 2004

Keywords

• nonn

Comments

Harmonic primes A092101 are a subset of these primes. Because these primes are analogous to the regular primes A007703 that divide the numerators of Bernoulli numbers, they might be called H-regular primes. The density of these primes is about 0.6 -- very close to the density of regular primes.

Links

• Eric Weisstein's World of Mathematics, Harmonic Number
• Eric Weisstein's World of Mathematics, Regular Prime

Crossrefs

Cf. A072984 (least k such that prime(n) divides A001008(k)).

Programs

Mathematica

n=1; Table[While[cnt=0; n++; p=Prime[n]; k=1; h=0; While[k<=(p-1)/2, h=h+1/k; If[Mod[Numerator[h], p]==0, cnt++ ]; k++ ]; cnt>0, ]; p, {100}]