A048684 Multiplicity of the maximum squarefree kernel function applied to the binomial coefficients C(n,k).

2, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 4, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			For n = 8, 9 or 10 the spectra of squarefree maximal divisors are {1,2,14,14,70,14,14,2,1}, {1,3,6,42,42,42,42,6,3,1} and {1,10,15,30,210,42,30,15,10,1}, respectively. The maxima (70,42 and 210) occur 1, 4 or 4 times. So a(8) = 1, a(9) = 4 and a(10) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A020233, A020738, A001221, A001222, A000005.

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;;, 1]]; a[n_] := Module[{r = rad /@ Table[Binomial[n, k], {k, 0, n}]}, Count[r, Max[r]]]; Array[a, 100] (* Amiram Eldar, Sep 17 2024 *)

PARI

rad(n) = vecprod(factor(n)[, 1]);
a(n) = {my(r = vector(n+1, k, rad(binomial(n,k-1))), rm = vecmax(r)); #select(x -> x==rm, r);} \\ Amiram Eldar, Sep 17 2024