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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A115751 A324888 A249145 * A191613 A298642 A243404

Adjacent sequences: A048681 A048682 A048683 * A048685 A048686 A048687

Keyword

nonn

Author

Labos Elemer

Status

approved