A074245 Numbers n such that sigma(n) is a harmonic number.

1, 5, 12, 76, 136, 139, 178, 269, 276, 308, 427, 429, 446, 455, 501, 581, 611, 612, 738, 932, 1576, 1637, 2952, 2969, 3184, 3204, 4647, 4975, 5400, 5458, 6199, 7152, 8816, 9120, 9180, 9196, 9272, 9294, 9504, 9584, 9720, 9950, 9960

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

Cf. A001599.

Sequence in context: A209340 A128323 A202203 * A235939 A215866 A219288

Adjacent sequences: A074242 A074243 A074244 * A074246 A074247 A074248

Keyword

nonn

Author

Joseph L. Pe, Sep 19 2002

Status

approved