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A082343 Numerator of sopfr(n)/n, where sopfr=A001414 is the sum of prime factors (with repetition).

%I A082343 #13 Dec 03 2021 04:19:59
%S A082343 0,1,1,1,1,5,1,3,2,7,1,7,1,9,8,1,1,4,1,9,10,13,1,3,2,15,1,11,1,1,1,5,
%T A082343 14,19,12,5,1,21,16,11,1,2,1,15,11,25,1,11,2,6,20,17,1,11,16,13,22,31,
%U A082343 1,1,1,33,13,3,18,8,1,21,26,1,1,1,1,39,13,23,18,3,1,13,4,43,1,1,22,45,32,17
%N A082343 Numerator of sopfr(n)/n, where sopfr=A001414 is the sum of prime factors (with repetition).
%C A082343 Denominator is A082344(n) = n/A082299(n).
%H A082343 Antti Karttunen, <a href="/A082343/b082343.txt">Table of n, a(n) for n = 1..65537</a>
%F A082343 a(n) = A001414(n)/A082299(n).
%e A082343 n=200: (2+2+2+5+5)/(2*2*2*5*5) = 16/(2*2*2*5*5) = (2*2*2*2)/(2*2*2*5*5) = 2/25, therefore a(200)=2, A082344(200)=25.
%t A082343 sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
%t A082343 a[n_] := Numerator[sopfr[n]/n];
%t A082343 Array[a, 100] (* _Jean-François Alcover_, Dec 03 2021 *)
%o A082343 (PARI)
%o A082343 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A082343 A082299(n) = gcd(n, A001414(n));
%o A082343 A082343(n) = A001414(n)/A082299(n); \\ _Antti Karttunen_, Mar 04 2018
%Y A082343 Cf. A001414, A082299, A082344.
%K A082343 nonn,frac
%O A082343 1,6
%A A082343 _Reinhard Zumkeller_, Apr 09 2003