login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074244 Numbers k such that phi(k) is a harmonic number. 1
1, 2, 7, 9, 14, 18, 29, 58, 213, 271, 284, 426, 542, 673, 731, 791, 833, 1011, 1015, 1017, 1131, 1305, 1346, 1348, 1376, 1462, 1508, 1568, 1582, 1624, 1666, 1720, 1960, 2022, 2030, 2034, 2064, 2088, 2262, 2352, 2436, 2580, 2610, 2940, 2971, 5942, 7775 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A205559 A047352 A184400 * A190565 A341631 A102994
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Sep 19 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 10:05 EST 2024. Contains 370294 sequences. (Running on oeis4.)