OFFSET
1,2
COMMENTS
Recall that n is harmonic if the harmonic mean of its divisors is an integer, i.e. if n * tau(n) / sigma(n) is an integer. (Tattersall, p. 147)
REFERENCES
Tattersall, J. "Elementary Number Theory in Nine Chapters", Cambridge Univ. Press, 2001.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
sigma(12) = 28 and 28 * tau(28) / sigma(28) = 28 * 6 / 56 = 3, an integer, so 12 is a term of the sequence.
MATHEMATICA
isHarmonic[n_] := IntegerQ[n*DivisorSigma[0, n] / DivisorSigma[1, n]]; Select[Range[10^4], isHarmonic[DivisorSigma[1, # ]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Sep 19 2002
STATUS
approved