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

1,2

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

Adjacent sequences: A063944 A063945 A063946 * A063948 A063949 A063950

Keyword

nonn,nice

Author

Wouter Meeussen, Sep 03 2001

Extensions

More terms from David W. Wilson, Sep 04 2001

Status

approved