

A175441


Denominators of the harmonic means H(n) of the first n positive integers.


7



1, 3, 11, 25, 137, 49, 363, 761, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, 2436559, 42142223, 14274301, 275295799, 11167027, 18858053, 19093197, 444316699, 1347822955
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OFFSET

1,2


COMMENTS

See A102928  numerators of the harmonic means of the first n positive integers.
a(n) = A001008(n) for n = 1  19 and other n.
a(n) is also the numerator of H(n)/(n+1)+1/(n+1)^2 = int(x^n*log(1x), x=0..1) with H(n) = A001008(x)/A002805(n) harmonic number of order n.  Groux Roland, Jan 08 2011
a(n) coincides with A001008(n) iff n is not in the sequence A256102. For the quotient A001008(n) / a(n) if n is from A256102 see the corresponding entry of A256103.  Wolfdieter Lang, Apr 23 2015


LINKS

Table of n, a(n) for n=1..24.


FORMULA

a(n) = numerator(sum(1/(k*(k+n)), k=1..oo)).  Paolo P. Lava, Jan 17 2013


EXAMPLE

H(n) = 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
Comparison with A001008: the first 19 entries coincide because 20 is the first entry of A256102; indeed, A001008(20) = 55835135 and a(2) = 11167027. The quotient is 5 = A256103(1).  Wolfdieter Lang, Apr 23 2015


CROSSREFS

Cf. A102928, A001008, A256102, A256103.
Sequence in context: A190476 A060746 A111935 * A001008 A231606 A096617
Adjacent sequences: A175438 A175439 A175440 * A175442 A175443 A175444


KEYWORD

nonn,easy


AUTHOR

Jaroslav Krizek, May 16 2010


STATUS

approved



