login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Maximum over k of the largest squarefree number dividing a value of binomial(n,k).
0

%I #11 May 20 2018 03:25:11

%S 1,2,3,6,10,15,35,70,42,210,462,462,858,3003,5005,4290,24310,24310,

%T 92378,125970,293930,646646,1352078,1352078,817190,5311735,2897310,

%U 13123110,34597290,17298645,100180065,200360130,129644790,2203961430

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

%e 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]

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

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

%K nonn

%O 1,2

%A _Labos Elemer_