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) = n / gcd(denominator(H(n)),n), where H(n) = sum(1/k, k=1..n). [Gary Detlefs, Sep 05 2011]
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