A379370 Denominators of the partial alternating sums of the reciprocals of the squarefree kernel function (A007947).

1, 2, 6, 3, 15, 30, 210, 105, 35, 70, 770, 1155, 15015, 30030, 2002, 1001, 17017, 102102, 1939938, 4849845, 4849845, 9699690, 223092870, 37182145, 37182145, 74364290, 223092870, 111546435, 3234846615, 2156564410, 66853496710, 33426748355, 100280245065, 200560490130

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.6, pp. 24-26.

Formula

a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A007947(k)).

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Denominator[Accumulate[Table[(-1)^(n+1)/rad[n], {n, 1, 50}]]]

Prog

(PARI) rad(n) = vecprod(factor(n)[, 1]);
list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / rad(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A007947, A073355, A370896, A379368, A379369 (numerators).

Sequence in context: A378679 A302033 A337643 * A380315 A071301 A145642

Adjacent sequences: A379367 A379368 A379369 * A379371 A379372 A379373

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 21 2024

Status

approved