cp's OEIS Frontend

A305054 If n = Product_i prime(x_i)^k_i, then a(n) = Sum_i k_i * omega(x_i), where omega = A001221 is number of distinct prime factors.

%I A305054 #8 Jun 09 2018 06:08:54
%S A305054 0,0,1,0,1,1,1,0,2,1,1,1,2,1,2,0,1,2,1,1,2,1,1,1,2,2,3,1,2,2,1,0,2,1,
%T A305054 2,2,2,1,3,1,1,2,2,1,3,1,2,1,2,2,2,2,1,3,2,1,2,2,1,2,2,1,3,0,3,2,1,1,
%U A305054 2,2,2,2,2,2,3,1,2,3,2,1,4,1,1,2,2,2,3
%N A305054 If n = Product_i prime(x_i)^k_i, then a(n) = Sum_i k_i * omega(x_i), where omega = A001221 is number of distinct prime factors.
%F A305054 Totally additive with a(prime(n)) = omega(n).
%F A305054 a(n) = A305053(n) + A001221(n). - _Michel Marcus_, Jun 09 2018
%t A305054 Table[If[n==1,0,Total@Cases[FactorInteger[n],{p_,k_}:>k*PrimeNu[PrimePi[p]]]],{n,100}]
%o A305054 (PARI) a(n) = {my(f=factor(n)); sum(k=1, #f~, f[k,2]*omega(primepi(f[k,1])));} \\ _Michel Marcus_, Jun 09 2018
%Y A305054 Cf. A001221, A003963, A056239, A076078, A112798, A286520, A290103, A302242, A304714, A304716, A305052, A305053.
%K A305054 nonn
%O A305054 1,9
%A A305054 _Gus Wiseman_, May 24 2018