OFFSET
1,1
COMMENTS
Therefore, apart from a(1) = 1, this sequence is a proper subset of A126706.
In the sequence R = {k = m*s : rad(m) | s, s > 1 in A120944}, there is a smallest term k such that g(k) <= 0 and a largest term k such that g(k) is positive. For instance, in A033845 where s = 6, only {6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864} are such that g(k) > 0.
For s > 1, an infinite number of k in R are such that g(k) is negative. For example, with s = 6, all terms k > 864 in A033845 are in this sequence.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
MATHEMATICA
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; Position[Table[r = rad[n]; DivisorSigma[0, n] - Count[Range[n/r], _?(Divisible[r, rad[#]] &)], {n, 5000}], _?(# < 0 &)][[All, 1]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jun 02 2024
STATUS
approved