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A335388
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Harmonic numbers (A001599) with a record number of divisors that are harmonic numbers.
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0
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1, 6, 140, 672, 30240, 332640, 2178540, 17428320, 163390500, 191711520, 326781000, 1307124000, 2701389600, 8104168800, 14378364000, 40520844000, 1175104476000, 7131668544000, 49921679808000
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OFFSET
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1,2
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COMMENTS
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The corresponding record values are 1, 2, 3, 4, 7, 9, 12, 15, 17, 19, 21, 25, 29, 34, 35, 43, 54, 75, 84.
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LINKS
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Table of n, a(n) for n=1..19.
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EXAMPLE
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1 has one divisor which is a harmonic number: 1. 6 has 2 divisors which are harmonic numbers: 1 and 6. The next harmonic number with more than 2 divisors which are harmonic numbers is 140 with 3 such divisors: 1, 28 and 140.
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MATHEMATICA
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h = Cases[Import["https://oeis.org/A001599/b001599.txt", "Table"], {_, _}][[;; , 2]]; hQ[n_] := Divisible[n * DivisorSigma[0, n], DivisorSigma[1, n]]; hsigma[n_] := DivisorSum[n, Boole @ hQ[#] &]; hm = 0; s = {}; Do[h1 = hsigma[h[[k]]]; If[h1 > hm, hm = h1; AppendTo[s, h[[k]]]], {k, 1, Length[h]}]; s
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CROSSREFS
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Cf. A001599, A335317.
Sequence in context: A342358 A122483 A335369 * A123729 A193835 A123728
Adjacent sequences: A335385 A335386 A335387 * A335389 A335390 A335391
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KEYWORD
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nonn,more
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AUTHOR
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Amiram Eldar, Jun 04 2020
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STATUS
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approved
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