OFFSET
1,2
COMMENTS
Recall that k is harmonic if the harmonic mean of its divisors is an integer, i.e. if k * tau(k) / sigma(k) is an integer (Tattersall, p. 147).
REFERENCES
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge Univ. Press, 2001.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)
EXAMPLE
phi(14) = 6 and 6 * tau(6) / sigma(6) = 6 * 4 / 12 = 2, an integer, so 14 is a term of the sequence.
MATHEMATICA
isHarmonic[n_] := IntegerQ[n*DivisorSigma[0, n] / DivisorSigma[1, n]]; Select[Range[10^4], isHarmonic[EulerPhi[ # ]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Sep 19 2002
STATUS
approved