A379360 - OEIS

%I #8 Dec 22 2024 16:52:37

%S 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 10,10,10,70,70,70,70,140,140,140,140,420,420,420,420,420,420,420,420,

%U 420,420,420,420,420,420,420,420,140,140,140,140,140,140,140,140

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

%D 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 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See section 5.1, Abelian group enumeration constants, p. 274.

%H Amiram Eldar, <a href="/A379360/b379360.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a(n) = denominator(Sum_{k=1..n} 1/A000688(k)).

%t Denominator[Accumulate[Table[1/FiniteAbelianGroupCount[n], {n, 1, 100}]]]

%o (PARI) f(n) = vecprod(apply(numbpart, factor(n)[, 2]));

%o list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / f(k); print1(denominator(s), ", "))};

%Y Cf. A000688, A063966, A370897, A379359 (numerators), A379362.

%K nonn,easy,frac

%O 1,4

%A _Amiram Eldar_, Dec 21 2024