

A102928


Reduced numerators of the harmonic means of the first n positive integers.


6



1, 4, 18, 48, 300, 120, 980, 2240, 22680, 25200, 304920, 332640, 4684680, 5045040, 5405400, 11531520, 208288080, 73513440, 1474352880, 62078016, 108636528, 113809696, 2736605872, 8566766208, 223092870000, 232016584800
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OFFSET

1,2


COMMENTS

See A175441  denominators of the harmonic means of the first n positive integers. [Jaroslav Krizek, May 16 2010]
a(n) is also the denominator of H(n1)/n + 1/n^2=int(x^n*log(1x),x=0..1) with H(n)= A001008(n)/A002805(n) the harmonic number of order n.  Groux Roland, Jan 08 2011
Equivalently, a(n) is the reduced denominator of the arithmetic mean of the reciprocals of the first n positive integers (corresponding reduced numerator is A175441(n)).  Rick L. Shepherd, Jun 15 2014
n divides a(n) iff n is not from the sequence A256102.  Wolfdieter Lang, Apr 23 2015


LINKS

Table of n, a(n) for n=1..26.
Eric Weisstein's World of Mathematics, Harmonic Mean


FORMULA

a(n) = denominator(EulerGamma/n + PolyGamma(0, 1 + n)/n). [Artur Jasinski, Nov 02 2008]
a(n) = numerator(n/H(n)), where H(n) is the nth harmonic number. [Gary Detlefs, Sep 10 2011]
a(n) = denominator(sum(1/(k*(k+n)), k=1..oo)). [Paolo P. Lava, Jan 17 2013]


EXAMPLE

1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
Division property: The first n not dividing a(n) is 20 because 20 = A256102(1). Indeed, a(20) = 62078016.  Wolfdieter Lang, Apr 23 2015


MATHEMATICA

Table[Denominator[Expand[EulerGamma/a + PolyGamma[0, 1 + a]/a]], {a, 1, 30}] (* Artur Jasinski, Nov 02 2008 *)
Table[Numerator[n/HarmonicNumber[n]], {n, 26}]


CROSSREFS

Cf. A001008.
Sequence in context: A027271 A073991 A052642 * A081528 A056147 A181857
Adjacent sequences: A102925 A102926 A102927 * A102929 A102930 A102931


KEYWORD

nonn,frac


AUTHOR

Eric W. Weisstein, Jan 19 2005


EXTENSIONS

Roland formula offset corrected by Gary Detlefs, Oct 06 2011


STATUS

approved



