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A349180
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Coreful harmonic numbers: nonsquarefree numbers k such that the harmonic mean of the coreful divisors of k is an integer.
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1
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12, 18, 36, 56, 60, 75, 84, 90, 126, 132, 150, 156, 168, 180, 198, 204, 228, 234, 240, 252, 276, 280, 306, 342, 348, 351, 372, 392, 396, 414, 420, 444, 450, 468, 492, 504, 516, 522, 525, 558, 564, 588, 612, 616, 630, 636, 660, 666, 684, 702, 708, 720, 726, 728
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OFFSET
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1,1
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COMMENTS
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A divisor of a number k is coreful if it is divisible by every prime that divides k.
The sequence is restricted to nonsquarefree numbers since the squarefree numbers have a single coreful divisor and thus they trivially have an integer harmonic mean.
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LINKS
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EXAMPLE
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12 is a term since its coreful divisors are 6 and 12 and their harmonic mean, 8, is an integer.
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MATHEMATICA
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rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; corHarmQ[n_] := Module[{r = rad[n], d}, d = Select[Divisors[n], rad[#] == r &]; IntegerQ[HarmonicMean[d]]]; Select[Range[10^3], !SquareFreeQ[#] && corHarmQ[#] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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