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A063947

Infinitary harmonic numbers: harmonic mean of infinitary divisors is an integer.

1, 6, 45, 60, 90, 270, 420, 630, 2970, 5460, 8190, 9100, 15925, 27300, 36720, 40950, 46494, 54600, 81900, 95550, 136500, 163800, 172900, 204750, 232470, 245700, 257040, 409500, 464940, 491400, 646425, 716625, 790398, 791700, 819000, 900900

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..239 (terms below 10^10)

P. Hagis, Jr. and G. L. Cohen, Infinitary harmonic numbers, Bull. Australian math. Soc., 41 (1990), 151-158 (Math. Rev. 91d:11001) (asymptotics).

Eric Weisstein's World of Mathematics, Harmonic Mean

Wikipedia, Harmonic mean

MATHEMATICA

bitty[ k_ ] := Union[ Flatten[ Outer[ Plus, Sequence @@ ({0, #} & /@ Union[ (2^Range[ 0, Floor[ Log[ 2, k ] ] ] ) Reverse[ IntegerDigits[ k, 2 ] ] ] ) ] ] ]; 1 + Flatten[ Position[ Table[ (Length[ # ] /(Plus @@ (1/#)) &)@ (Apply[ Times, (First[ it ] ^ (# /. z -> List)) ] & /@ Flatten[ Outer[ z, Sequence @@ (bitty /@ Last[ it = Transpose[ FactorInteger[ k ] ] ] ), 1 ] ]), {k, 2, 2^22 + 1} ], _Integer ] ] (* Robert G. Wilson v, Sep 04 2001 *)

PROG

(Haskell)

import Data.Ratio (denominator)

import Data.List (genericLength)

a063947 n = a063947_list !! (n-1)

a063947_list = filter ((== 1) . denominator . hm . a077609_row) [1..]

where hm xs = genericLength xs / sum (map (recip . fromIntegral) xs)

-- Reinhard Zumkeller, Jul 10 2013

CROSSREFS

Cf. A037445, A049417.

Cf. A077609.

Sequence in context: A367561 A286325 A335387 * A006086 A273507 A131513