A379362 Denominators of the partial alternating 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, 15, 30, 30, 30, 30, 210, 210, 210, 210, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 420, 140, 140, 420, 420, 420, 420, 420, 420, 420

Offset

1,4

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)^(k+1)/A000688(k)).

Mathematica

Denominator[Accumulate[Table[(-1)^(n+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)^(k+1) / f(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A000688, A063966, A370897, A379360, A379361 (numerators).

Sequence in context: A096625 A359072 A379360 * A263455 A283677 A355192

Adjacent sequences: A379359 A379360 A379361 * A379363 A379364 A379365

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 21 2024

Status

approved