infinitary harmonic numbers needed
N. J. A. Sloane
njas at research.att.com
Wed Aug 29 04:45:01 CEST 2001
Dear Seqfans
there's a sequence that maybe someone could compute
To start with, recall that there are numbers that are
called the infinitary divisors of n
Their sum gives A049417,
the number of infinitary divisors gives A037445.
They are defined there and (maybe clearer) in A006407
ok, so take n, make a list of its infinitary divisors,
(call them d_1, d_2, ... d_k)
compute their harmonic mean, which is
1 / ( (1/k) * (Sum 1/d_i ) )
The sequence i'm interested in is the set of n for which
this harmonic mean is an integer.
There's a paper, Infinitary harmonic numbers,
by Hagis and Cohen, Math. Rev. 91d:11001,
Bull. Australian math. Soc., 41 (1990), 151-158
that discusses their their asymptotics.
If you have access to math sci net, see
http://www.ams.org/msnmain?co3=AND&co4=AND&dr=all&fmt=doc&fn=105&id=91d_11001&l=100&pg3=ICN&pg4=TI&r=2&s3=Cohen&s4=infinitary
The sequence may be in the EIS already under a different name.
NJAS
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