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 A335318 Harmonic numbers (A001599) k with a record abundancy index sigma(k)/k. 2
 1, 6, 140, 270, 672, 8190, 30240, 332640, 14303520, 17428320, 27027000, 191711520, 2144862720, 3506025600, 5943057120, 14378364000, 45578332800, 288662774400, 505159855200, 2020639420800, 10680522652800, 54557264361600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding record values are 1, 2, 2.4, 2.666..., 3, 3.2, 4, 4.363..., ... The terms 1, 6, 672 and 30240 are multiply perfect numbers (A007691) with abundancy indices 1, 2, 3, and 4, respectively. There is no 5-multiperfect number (A046060) in this sequence since A046060(1) = 14182439040 is larger than the harmonic number 5943057120 which is 5-abundant, having an abundancy index 5.067... LINKS EXAMPLE The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their abundancy indices are 1, 2, 2, 2.4, 2.666..., 2 and 3. The record values, 1, 2, 2.4, 2.666... and 3 occur at 1, 6, 140, 270 and 672, the first 5 terms of this sequence. MATHEMATICA rm = 0; s = {}; Do[h = DivisorSigma[0, n]/(r = DivisorSigma[1, n]/n); If[IntegerQ[h] && r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^6}]; s CROSSREFS Cf. A000203, A001599, A335316, A335317. Sequence in context: A288565 A090944 A007340 * A342358 A122483 A335369 Adjacent sequences:  A335315 A335316 A335317 * A335319 A335320 A335321 KEYWORD nonn,more AUTHOR Amiram Eldar, May 31 2020 STATUS approved

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Last modified June 16 16:09 EDT 2021. Contains 345063 sequences. (Running on oeis4.)