The numerators are A001008, and the denominators are A002805. The denominators are the easy part, so I'll mostly address that. The q(n)'s definitely have atypical factorizations; in particular, q(n) divides n!. (In fact, it divides lcm(1,2,3,...,n).) Note that if p is prime, q(p^k) is always divisible by p^k (in fact, q(n) is divisible by p^k for p^k <= n < 2*p^k - you can improve this result further for p != 3). The numerators are also divisible by every p (except 2): see http://mathworld.wolfram.com/WolstenholmesTheorem.html/. Franklin T. Adams-Watters -----Original Message----- From: dasimov@earthlink.net The harmonic number H(n) := 1 + 1/2 + 1/3 + . . . + 1/n has the interesting property that although it -> oo as n does, it's never an integer. So let H(n) = p(n)/q(n) in lowest terms. (I have full confidence that p and q are already in the OEIS.) What is known about the factorizations of the p(n)'s and q(n)'s ? In particular, are their factorizations known or believed to have statistical properties atypical of numbers of the same size (re the number, size, and exponents of their prime factors) ? Do the factors of p(n) (or q(n)) have special number-theoretical properties? (I.e., what is known about the primes -- if any -- that *never* occur as a factor of any p(n) (q(n)) ? --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.