

A074245


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


1



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
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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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



