OFFSET
1,5
COMMENTS
It is well-known that prime p >= 3 divides the numerator of H(p-1). For primes p in A092194, there are integers k < p-1 for which p divides the numerator of H(k). Interestingly, if p divides A001008(k) for k < p-1, then p divides A001008(p-k-1). Hence the terms of this sequence are usually even. The only exceptions are the two known Wieferich primes 1093 and 3511, A001220, which have 3 values of k < p-1 for which p divides A001008(k), one being k = (p-1)/2.
LINKS
T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Wieferich Prime
EXAMPLE
a(5) = 2 because 11 = prime(5) and there are 2 values, k = 3 and 7, such that 11 divides A001008(k).
MATHEMATICA
len=500; Table[p=Prime[i]; cnt=0; k=1; While[k<p-1, If[Mod[Numerator[HarmonicNumber[k]], p]==0, cnt++ ]; k++ ]; cnt, {i, len}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 01 2004
STATUS
approved