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A369911 a(n) = Sum_{p|n, p prime} p * sopf(n/p).

%I A369911 #10 Jul 10 2025 12:55:44
%S A369911 0,0,0,4,0,12,0,4,9,20,0,16,0,28,30,4,0,21,0,24,42,44,0,16,25,52,9,32,
%T A369911 0,62,0,4,66,68,70,25,0,76,78,24,0,82,0,48,39,92,0,16,49,45,102,56,0,
%U A369911 21,110,32,114,116,0,66,0,124,51,4,130,122,0,72,138,118,0,25
%N A369911 a(n) = Sum_{p|n, p prime} p * sopf(n/p).
%C A369911 Dirichlet convolution of A061397(n) and A008472(n). - _Wesley Ivan Hurt_, Jul 10 2025
%H A369911 Antti Karttunen, <a href="/A369911/b369911.txt">Table of n, a(n) for n = 1..20000</a>
%F A369911 From _Wesley Ivan Hurt_, Jul 10 2025: (Start)
%F A369911 a(n) = Sum_{d|n} A061397(d) * A008472(n/d).
%F A369911 a(p^k) = p^2 * (1-floor(1/k)) for p prime and k>=1. (End)
%t A369911 a[n_] := Sum[p, {p, Select[Divisors[n], PrimeQ]}]; Table[DivisorSum[n, #*a[n/#] &, PrimeQ[#] &], {n, 100}]
%o A369911 (PARI)
%o A369911 A008472(n) = vecsum(factor(n)[, 1]);
%o A369911 A369911(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i,1]*A008472(n/f[i, 1]))); \\ _Antti Karttunen_, Jan 23 2025
%Y A369911 Cf. A008472 (sopf), A061397, A369744.
%K A369911 nonn,easy
%O A369911 1,4
%A A369911 _Wesley Ivan Hurt_, Feb 05 2024