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

Offset: 1

Author

Wouter Meeussen, Sep 03 2001

Keywords

• nonn
• nice

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

Crossrefs

Cf. A037445, A049417.

Cf. A077609.

Programs

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

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 *)

Extensions

More terms from David W. Wilson, Sep 04 2001