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

1,2

Links

Table of n, a(n) for n=1..34.

Example

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]

Prog

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

Crossrefs

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

Sequence in context: A370819 A055789 A238891 * A051891 A108062 A347117

Adjacent sequences: A048678 A048679 A048680 * A048682 A048683 A048684

Keyword

nonn

Author

Labos Elemer

Status

approved