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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
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
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
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jun 26 2006
STATUS
approved