infinitary divisors (A037445, A049417)

[N. J. A. Sloane]

Dear Wouter,

I don't understand mathematica, but it looks like all
your calculations are correct!


i will add your extension to A049417, and your new sequence
of the harmonic numbers

(I quote)

their harmonic mean is integer for k= :

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,2,2^16+1}] ,_Integer]] //Timing

{238.9*Second,
 {6, 45, 60, 90, 270, 420, 630, 2970, 5460, 8190, 9100, 15925, 27300, 36720,
40950, 46494, 54600}}


(end of quote)


Thanks very much for computing this.


Regards

Neil