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A344226 a(n) = Sum_{d|n} n^omega(d) / d.

%I A344226 #14 May 16 2021 07:58:43
%S A344226 1,2,2,4,2,12,2,8,5,18,2,50,2,24,24,16,2,90,2,80,32,36,2,198,7,42,14,
%T A344226 110,2,1232,2,32,48,54,48,476,2,60,56,324,2,2310,2,170,210,72,2,782,9,
%U A344226 338,72,200,2,756,72,450,80,90,2,12558,2,96,290,64,84,5474,2,260,96,5940
%N A344226 a(n) = Sum_{d|n} n^omega(d) / d.
%H A344226 Seiichi Manyama, <a href="/A344226/b344226.txt">Table of n, a(n) for n = 1..10000</a>
%F A344226 a(n) = (1/n) * Sum_{k=1..n} tau(gcd(k,n)^n).
%F A344226 a(n) = (1/n) * Sum_{d|n} phi(n/d) * tau(d^n).
%F A344226 If p is prime, a(p) = 2.
%t A344226 Table[DivisorSum[n,n^PrimeNu@#/#&],{n,100}] (* _Giorgos Kalogeropoulos_, May 13 2021 *)
%o A344226 (PARI) a(n) = sumdiv(n, d, n^omega(d)/d);
%o A344226 (PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n)^n))/n;
%o A344226 (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d^n))/n;
%Y A344226 Cf. A062319, A344223.
%K A344226 nonn
%O A344226 1,2
%A A344226 _Seiichi Manyama_, May 12 2021