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A379360 Denominators of the partial sums of the reciprocals of the number of abelian groups function (A000688).

%I A379360 #8 Dec 22 2024 16:52:37
%S A379360 1,1,1,2,2,2,2,6,3,3,3,6,6,6,6,30,30,15,15,30,30,30,30,30,15,15,5,10,
%T A379360 10,10,10,70,70,70,70,140,140,140,140,420,420,420,420,420,420,420,420,
%U A379360 420,420,420,420,420,420,420,420,140,140,140,140,140,140,140,140
%N A379360 Denominators of the partial sums of the reciprocals of the number of abelian groups function (A000688).
%D A379360 Jean-Marie De Koninck and Aleksandar Ivić, Topics in Arithmetical Functions, North-Holland Publishing Company, Amsterdam, Netherlands, 1980. See pp. 13-16, Theorem 1.3.
%D A379360 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See section 5.1, Abelian group enumeration constants, p. 274.
%H A379360 Amiram Eldar, <a href="/A379360/b379360.txt">Table of n, a(n) for n = 1..10000</a>
%H A379360 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 4.8, pp. 27-28.
%F A379360 a(n) = denominator(Sum_{k=1..n} 1/A000688(k)).
%t A379360 Denominator[Accumulate[Table[1/FiniteAbelianGroupCount[n], {n, 1, 100}]]]
%o A379360 (PARI) f(n) = vecprod(apply(numbpart, factor(n)[, 2]));
%o A379360 list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / f(k); print1(denominator(s), ", "))};
%Y A379360 Cf. A000688, A063966, A370897, A379359 (numerators), A379362.
%K A379360 nonn,easy,frac
%O A379360 1,4
%A A379360 _Amiram Eldar_, Dec 21 2024