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

1,4

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.

Formula

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

Mathematica

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

Prog

(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), ", "))};

Crossrefs

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

Sequence in context: A334512 A096625 A359072 * A379362 A263455 A283677

Adjacent sequences: A379357 A379358 A379359 * A379361 A379362 A379363

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 21 2024

Status

approved