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
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.
Programs
-
Mathematica
rad[n_] := Times @@ FactorInteger[n][[;;, 1]]; Denominator[Accumulate[Table[(-1)^(n+1)/rad[n], {n, 1, 50}]]] -
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), ", "))};
Formula
a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A007947(k)).