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Dirichlet convolution of Dedekind psi function with reduced totient function.
2

%I #10 Sep 20 2023 15:59:16

%S 1,4,6,11,10,24,14,26,26,40,22,64,26,56,56,58,34,104,38,106,78,88,46,

%T 148,74,104,102,148,58,224,62,128,122,136,128,272,74,152,144,244,82,

%U 312,86,232,232,184,94,326,146,296,188,274,106,408,200,340,210,232,118

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

%F a(n) = Sum{d|n} A001615(d) * A002322(n/d).

%F a(p) = A365648(p) where p is a term of A000040.

%t psi[n_Integer] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Table[DirichletConvolve[psi[k], CarmichaelLambda[k], k, n], {n, 1, 100}] (* _Amiram Eldar_, Sep 15 2023 *)

%o (Python)

%o from sympy import divisors, primefactors, prod, reduced_totient

%o def psi(n):

%o return n*prod(p+1 for p in primefactors(n))//prod(primefactors(n))

%o def a(n): return sum(psi(d) * reduced_totient(n//d) for d in divisors(n))

%Y Cf. A000040, A001615, A002322, A365648.

%K nonn

%O 1,2

%A _Torlach Rush_, Sep 14 2023