A379370 - OEIS

%I #6 Dec 22 2024 16:54:17

%S 1,2,6,3,15,30,210,105,35,70,770,1155,15015,30030,2002,1001,17017,

%T 102102,1939938,4849845,4849845,9699690,223092870,37182145,37182145,

%U 74364290,223092870,111546435,3234846615,2156564410,66853496710,33426748355,100280245065,200560490130

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

%H Amiram Eldar, <a href="/A379370/b379370.txt">Table of n, a(n) for n = 1..1000</a>

%H László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.6, pp. 24-26.

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

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

%o (PARI) rad(n) = vecprod(factor(n)[, 1]);

%o list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / rad(k); print1(denominator(s), ", "))};

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

%K nonn,easy,frac

%O 1,2

%A _Amiram Eldar_, Dec 21 2024