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A379141 If n = Product (p_j^k_j) then a(n) = numerator of Sum 1/k_j.

%I A379141 #15 Jan 14 2025 01:50:24
%S A379141 0,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,3,2,2,1,4,1,2,1,3,1,3,1,1,2,2,
%T A379141 2,1,1,2,2,4,1,3,1,3,3,2,1,5,1,3,2,3,1,4,2,4,2,2,1,5,1,2,3,1,2,3,1,3,
%U A379141 2,3,1,5,1,2,3,3,2,3,1,5,1,2,1,5,2,2,2,4,1,5,2,3,2,2,2,6,1,3,3,1,1,3,1,4,3,2,1,5,1,3
%N A379141 If n = Product (p_j^k_j) then a(n) = numerator of Sum 1/k_j.
%H A379141 Robert Israel, <a href="/A379141/b379141.txt">Table of n, a(n) for n = 1..10000</a>
%p A379141 a:= n-> numer(add(1/i[2], i=ifactors(n)[2])):
%p A379141 seq(a(n), n=1..110);  # _Alois P. Heinz_, Dec 16 2024
%t A379141 Join[{0}, Table[Plus @@ (1/#[[2]] & /@ FactorInteger[n]), {n, 2, 110}]] // Numerator
%o A379141 (PARI) a(n) = my(f=factor(n)); numerator(sum(k=1, #f~, 1/f[k,2])); \\ _Michel Marcus_, Dec 16 2024
%Y A379141 Cf. A001222, A005361, A028235, A028236.
%K A379141 nonn,frac
%O A379141 1,6
%A A379141 _Ilya Gutkovskiy_, Dec 16 2024