A379360 Denominators of the partial sums of the reciprocals of the number of abelian groups function (A000688).
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, 10, 10, 10, 70, 70, 70, 70, 140, 140, 140, 140, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 140, 140, 140, 140, 140, 140, 140, 140
Offset: 1
References
- 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.
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See section 5.1, Abelian group enumeration constants, p. 274.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.8, pp. 27-28.
Programs
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Mathematica
Denominator[Accumulate[Table[1/FiniteAbelianGroupCount[n], {n, 1, 100}]]] -
PARI
f(n) = vecprod(apply(numbpart, factor(n)[, 2])); list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / f(k); print1(denominator(s), ", "))};
Formula
a(n) = denominator(Sum_{k=1..n} 1/A000688(k)).