A082343 - OEIS

%I #13 Dec 03 2021 04:19:59

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

%C Denominator is A082344(n) = n/A082299(n).

%H Antti Karttunen, <a href="/A082343/b082343.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A001414(n)/A082299(n).

%e 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 sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];

%t a[n_] := Numerator[sopfr[n]/n];

%t Array[a, 100] (* _Jean-François Alcover_, Dec 03 2021 *)

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

%o A082299(n) = gcd(n, A001414(n));

%o A082343(n) = A001414(n)/A082299(n); \\ _Antti Karttunen_, Mar 04 2018

%Y Cf. A001414, A082299, A082344.

%K nonn,frac

%O 1,6

%A _Reinhard Zumkeller_, Apr 09 2003