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 A093569 For p = prime(n), the number of integers k < p-1 such that p divides A001008(k), the numerator of the harmonic number H(k). 2
 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)