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A369744 a(n) = Sum_{p|n, p prime} p * omega(n/p).

%I A369744 #22 Jul 10 2025 13:41:36
%S A369744 0,0,0,2,0,5,0,2,3,7,0,7,0,9,8,2,0,8,0,9,10,13,0,7,5,15,3,11,0,20,0,2,
%T A369744 14,19,12,10,0,21,16,9,0,24,0,15,11,25,0,7,7,12,20,17,0,8,16,11,22,31,
%U A369744 0,22,0,33,13,2,18,32,0,21,26,28,0,10,0,39,13,23,18,36
%N A369744 a(n) = Sum_{p|n, p prime} p * omega(n/p).
%C A369744 Dirichlet convolution of A061397(n) and A001221(n). - _Wesley Ivan Hurt_, Apr 24 2025
%H A369744 Antti Karttunen, <a href="/A369744/b369744.txt">Table of n, a(n) for n = 1..20000</a>
%F A369744 a(p^k) = 1 for p prime and k = 1, else p if k >= 2. - _Wesley Ivan Hurt_, Jun 26 2024
%F A369744 a(n) = Sum_{d|n} d * omega(n/d) * c(d), where c = A010051. - _Wesley Ivan Hurt_, Apr 15 2025
%t A369744 Table[DivisorSum[n, #*PrimeNu[n/#] &, PrimeQ[#] &], {n, 100}]
%o A369744 (PARI) A369744(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i,1]*omega(n/f[i, 1]))); \\ _Antti Karttunen_, Jan 23 2025
%Y A369744 Cf. A001221 (omega), A010051, A061397, A323599, A345354, A345355.
%Y A369744 Cf. also A369911.
%K A369744 nonn,easy
%O A369744 1,4
%A A369744 _Wesley Ivan Hurt_, Jan 30 2024