A048681 Maximum over k of the largest squarefree number dividing a value of binomial(n,k).

1, 2, 3, 6, 10, 15, 35, 70, 42, 210, 462, 462, 858, 3003, 5005, 4290, 24310, 24310, 92378, 125970, 293930, 646646, 1352078, 1352078, 817190, 5311735, 2897310, 13123110, 34597290, 17298645, 100180065, 200360130, 129644790, 2203961430

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			For n=10, the squarefree kernels of binomial(n,k) are {1, 10, 15, 30, 210, 42, 210, 30, 15, 10, 1}, so the maximal largest squarefree divisor is that of binomial(10,4)=210: it is 210, so a(10)=210. (It is not equal to the largest squarefree number dividing binomial(10,5)=252, which is A048633(10)=42.) [edited by _Jon E. Schoenfield_, May 19 2018]
		

Crossrefs

Analogous sequences for A001221, A001222, A000005 are given in A048273, A048275, A048620.

Programs

PARI

a(n) = vecmax(vector(ceil(n\2)+1, k, factorback(factorint(binomial(n,k-1))[, 1]))); \\ Michel Marcus, May 20 2018