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Denominators of the partial sums of the reciprocals of the Dedekind psi function (A001615).
1

%I #9 Oct 15 2022 07:19:28

%S 1,3,12,4,12,1,8,24,24,72,72,36,252,504,126,504,504,504,2520,840,3360,

%T 10080,10080,10080,2016,2016,2016,2016,10080,10080,5040,1260,5040,

%U 15120,7560,3780,71820,17955,143640,17955,35910,574560,6320160,6320160,6320160,6320160

%N Denominators of the partial sums of the reciprocals of the Dedekind psi function (A001615).

%C See A357818 for more details.

%F a(n) = denominator(Sum_{k=1..n} 1/psi(k)).

%t psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); psi[1] = 1; Denominator[Accumulate[1/Array[psi[#] &, 50]]]

%o (PARI) f(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615

%o a(n) = denominator(sum(k=1, n, 1/f(k))); \\ _Michel Marcus_, Oct 15 2022

%Y Cf. A001615, A173290, A357818 (numerators).

%Y Similar sequences: A048049, A104529, A212718.

%K nonn,frac

%O 1,2

%A _Amiram Eldar_, Oct 14 2022