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 A120263 Ratio of the numerator of n*HarmonicNumber[n] to the numerator of HarmonicNumber[n]: A096617(n)/A001008(n). 1
 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(n) is not equal to 1 when n belongs to A074791 - numbers n such that n does not divide the denominator of the n-th harmonic number. a(n) is almost always equal to 1 except for n=6,18,20,21,33,42,54,.. when a(n) seems to be equal to a prime divisor of n. a(n) could be equal to a squared prime divisor of n as for n=100,294,500,847,.. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A096617(n)/A001008(n) = numerator[n*Sum[1/i,{i,1,n}]] / numerator[Sum[1/i,{i,1,n}]]. a(n) = n / gcd(denominator(H(n)),n), where H(n) = sum(1/k, k=1..n). [Gary Detlefs, Sep 05 2011] a(n) = A096617(n)*A110566(n)/A025529(n). [Arkadiusz Wesolowski, Mar 29 2012] MATHEMATICA Numerator[Table[n*Sum[1/i, {i, 1, n}], {n, 1, 500}]]/Numerator[Table[Sum[1/i, {i, 1, n}], {n, 1, 500}]] PROG (PARI) {h(n) = sum(k=1, n, 1/k)}; for(n=1, 100, print1(numerator(n*h(n))/numerator(h(n)), ", ")) \\ G. C. Greubel, Sep 01 2018 (Magma) [Numerator(n*HarmonicNumber(n))/Numerator(HarmonicNumber(n)): n in [1..100]]; // G. C. Greubel, Sep 01 2018 CROSSREFS Cf. A096617, A001008, A074791. Sequence in context: A097031 A354997 A327537 * A250208 A325825 A030580 Adjacent sequences: A120260 A120261 A120262 * A120264 A120265 A120266 KEYWORD frac,nonn AUTHOR Alexander Adamchuk, Jun 26 2006 STATUS approved

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)