login
A063947
Infinitary harmonic numbers: harmonic mean of infinitary divisors is an integer.
17
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. A077609.
Sequence in context: A367561 A286325 A335387 * A006086 A273507 A131513
KEYWORD
nonn,nice
AUTHOR
Wouter Meeussen, Sep 03 2001
EXTENSIONS
More terms from David W. Wilson, Sep 04 2001
STATUS
approved