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A074244
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Numbers n such that phi(n) is a harmonic number.
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0
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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; internal format)
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OFFSET
| 1,2
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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)
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REFERENCES
| Tattersall, J. "Elementary Number Theory in Nine Chapters", Cambridge Univ. Press, 2001.
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EXAMPLE
| phi(14) = 6 and 6 * tau(6) / sigma(6) = 6 * 4 / 12 = 2, an integer, so 14 is a term of the sequence.
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MATHEMATICA
| isHarmonic[n_] := IntegerQ[n*DivisorSigma[0, n] / DivisorSigma[1, n]]; Select[Range[10^4], isHarmonic[EulerPhi[ # ]] &]
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CROSSREFS
| Cf. A001599.
Sequence in context: A205559 A047352 A184400 * A190565 A102994 A168132
Adjacent sequences: A074241 A074242 A074243 * A074245 A074246 A074247
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Sep 19 2002
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