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A074245 Numbers n such that sigma(n) is a harmonic number. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..43.

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

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)