A074244 Numbers k such that phi(k) is a harmonic number.

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

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

Cf. A000010, A001599.

Sequence in context: A205559 A047352 A184400 * A190565 A341631 A102994

Adjacent sequences: A074241 A074242 A074243 * A074245 A074246 A074247

Keyword

nonn

Author

Joseph L. Pe, Sep 19 2002

Status

approved