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 A335388 Harmonic numbers (A001599) with a record number of divisors that are harmonic numbers. 0
 1, 6, 140, 672, 30240, 332640, 2178540, 17428320, 163390500, 191711520, 326781000, 1307124000, 2701389600, 8104168800, 14378364000, 40520844000, 1175104476000, 7131668544000, 49921679808000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding record values are 1, 2, 3, 4, 7, 9, 12, 15, 17, 19, 21, 25, 29, 34, 35, 43, 54, 75, 84. LINKS EXAMPLE 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. MATHEMATICA 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 CROSSREFS Cf. A001599, A335317. Sequence in context: A342358 A122483 A335369 * A123729 A193835 A123728 Adjacent sequences: A335385 A335386 A335387 * A335389 A335390 A335391 KEYWORD nonn,more AUTHOR Amiram Eldar, Jun 04 2020 STATUS approved

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Last modified February 3 04:55 EST 2023. Contains 360024 sequences. (Running on oeis4.)