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
Keywords
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
Programs
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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