A379369 Numerators of the partial alternating sums of the reciprocals of the squarefree kernel function (A007947).

1, 1, 5, 1, 8, 11, 107, 1, 12, 17, 257, 193, 3664, 5183, 479, -261, -3436, -37633, -612925, -2017297, -1786352, -4013599, -82613087, -19965872, -12529443, -27919051, -9392863, -12664034, -255710551, -242359181, -5356570201, -19391659278, -55136182529, -116171203003

Offset

1,3

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

a(n)/A379370(n) ~ -A379367(n)/A379368(n).

Example

Fractions begin with 1, 1/2, 5/6, 1/3, 8/15, 11/30, 107/210, 1/105, 12/35, 17/70, 257/770, 193/1155, ...

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Numerator[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(numerator(s), ", "))};

Crossrefs

Cf. A007947, A073355, A370896, A379367, A379368, A379370 (denominators).

Sequence in context: A269229 A193089 A154310 * A193856 A255294 A115521

Adjacent sequences: A379366 A379367 A379368 * A379370 A379371 A379372

Keyword

sign,easy,frac

Author

Amiram Eldar, Dec 21 2024

Status

approved