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A379368 Denominators of the partial sums of the reciprocals of the squarefree kernel function (A007947).

%I A379368 #6 Dec 22 2024 16:54:02
%S A379368 1,2,6,3,15,10,70,35,105,210,2310,385,5005,10010,30030,15015,255255,
%T A379368 510510,9699690,4849845,4849845,9699690,223092870,111546435,22309287,
%U A379368 44618574,44618574,3187041,92424189,308080630,9550499530,4775249765,1302340845,2604681690,18232771830
%N A379368 Denominators of the partial sums of the reciprocals of the squarefree kernel function (A007947).
%D A379368 Jean-Marie De Koninck and Aleksandar Ivić, Topics in Arithmetical Functions, North-Holland Publishing Company, Amsterdam, Netherlands, 1980. See pp. 16-17.
%H A379368 Amiram Eldar, <a href="/A379368/b379368.txt">Table of n, a(n) for n = 1..1000</a>
%H A379368 N. G. de Bruijn, <a href="https://doi.org/10.1215/ijm/1255631814">On the number of integers <= x whose prime factors divide n</a>, Illinois Journal of Mathematics, Vol. 6, No. 1 (1962), pp. 137-141.
%H A379368 Olivier Robert and Gérald Tenenbaum, <a href="https://doi.org/10.1016/j.indag.2013.07.007">Sur la répartition du noyau d'un entier</a>, Indagationes Mathematicae, Vol. 24, No. 4 (2013), pp. 802-914.
%H A379368 László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.6, pp. 24-26.
%F A379368 a(n) = denominator(Sum_{k=1..n} 1/A007947(k)).
%t A379368 rad[n_] := Times @@ FactorInteger[n][[;;, 1]]; Denominator[Accumulate[Table[1/rad[n], {n, 1, 50}]]]
%o A379368 (PARI) rad(n) = vecprod(factor(n)[, 1]);
%o A379368 list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / rad(k); print1(denominator(s), ", "))};
%Y A379368 Cf. A007947, A073355, A370896, A379367 (numerators), A379370.
%K A379368 nonn,easy,frac
%O A379368 1,2
%A A379368 _Amiram Eldar_, Dec 21 2024