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Numerator of average of prime factors of n.
16

%I #5 Oct 15 2017 01:00:22

%S 2,3,2,5,5,7,2,3,7,11,7,13,9,4,2,17,8,19,3,5,13,23,9,5,15,3,11,29,10,

%T 31,2,7,19,6,5,37,21,8,11,41,4,43,5,11,25,47,11,7,4,10,17,53,11,8,13,

%U 11,31,59,3,61,33,13,2,9,16,67,7,13,14,71,12,73,39,13,23,9,6,79,13,3,43,83,7

%N Numerator of average of prime factors of n.

%H G. C. Greubel, <a href="/A123528/b123528.txt">Table of n, a(n) for n = 2..5000</a>

%F a(n) = sopfr(n) / bigomega(n) = A001414(n) / A001222(n).

%e 12 = 2 * 2 * 3, so a(12) = (2 + 2 + 3) / 3 = 7/3.

%e Sequence of fractions starts 2/1, 3/1, 2/1, 5/1, 5/2, 7/1, 2/1, 3/1, 7/2, 11/1, 7/3.

%t f[n_] := Plus @@ Times @@@ FactorInteger@n; f[1] = 0; Numerator[ Table[ f[n]/PrimeOmega[n], {n, 2, 50}]] (* _G. C. Greubel_, Oct 14 2017 *)

%Y Cf. A123529, A067629, A001414, A001222.

%K frac,nonn

%O 2,1

%A _Franklin T. Adams-Watters_, Oct 02 2006