A369601 - OEIS

%I #8 Feb 05 2024 11:36:15

%S 1,2,4,5,8,8,12,10,16,16,20,18,24,24,28,22,32,32,36,36,42,40,44,36,56,

%T 48,60,54,56,56,60,48,70,64,84,70,72,72,84,72,80,84,84,90,108,88,92,

%U 78,120,112,112,108,104,120,140,108

%N Dirichlet convolution of totient function with reduced totient function.

%F a(n) = Sum_{d|n} A000010(d) * A002322(n/d).

%e a(4) = phi(1)*lambda(4) + phi(2)*lambda(2) + phi(4)*lambda(1) = 5, where lambda is Carmichael's reduced totient function.

%t a[n_]:=Sum[EulerPhi[d]CarmichaelLambda[n/d],{d,Divisors[n]}]; Array[a,56] (* _Stefano Spezia_, Jan 27 2024 *)

%o (PARI) a(n) = sumdiv(n,d,eulerphi(d)*lcm(znstar(n/d)[2]))

%Y Cf. A000010, A002322.

%K nonn,easy

%O 1,2

%A _Miles Englezou_, Jan 26 2024