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%I #8 Jul 02 2021 03:49:00
%S 1,2,2,3,2,1,2,4,3,1,2,6,2,1,1,5,2,6,2,6,1,1,2,4,3,1,4,6,2,2,2,6,1,1,
%T 1,3,2,1,1,4,2,2,2,6,6,1,2,10,3,6,1,6,2,4,1,4,1,1,2,3,2,1,6,7,1,2,2,6,
%U 1,2,2,12,2,1,6,6,1,2,2,10,5,1,2,3,1,1
%N a(n) is the denominator of the average number of distinct prime factors of the divisors of n.
%C See A346009 for details.
%H Amiram Eldar, <a href="/A346010/b346010.txt">Table of n, a(n) for n = 1..10000</a>
%H R. L. Duncan, <a href="https://www.jstor.org/stable/2311587">Note on the divisors of a number</a>, The American Mathematical Monthly, Vol. 68, No. 4 (1961), pp. 356-359.
%H Sébastien Gaboury, <a href="http://hdl.handle.net/20.500.11794/18899">Sur les convolutions de fonctions arithmétiques</a>, M.Sc. thesis, Laval University, Quebec, 2007.
%t a[n_] := Denominator[DivisorSum[n, PrimeNu[#] &]/DivisorSigma[0, n]]; Array[a, 100]
%t (* or *)
%t f[p_, e_] := e/(e+1); a[1] = 1; a[n_] := Denominator[Plus @@ f @@@ FactorInteger[n]]; Array[a, 100]
%Y Cf. A346009 (numerators).
%K nonn,frac
%O 1,2
%A _Amiram Eldar_, Jul 01 2021
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