A080396 Largest squarefree numbers dividing the binomial coefficients C(n,k) read by row, 0<=k<=n. Squarefree kernel of Pascal triangle.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 6, 2, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 10, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 2, 14, 14, 70, 14, 14, 2, 1, 1, 3, 6, 42, 42, 42, 42, 6, 3, 1, 1, 10, 15, 30, 210, 42, 210, 30, 15, 10, 1, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 1, 6, 66

Offset: 0

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1,
1,1,
1,2,1,
1,3,3,1,
1,2,6,2,1,
1,5,10,10,5,1,
1,6,15,10,15,6,1, ...
		

Crossrefs

Cf. A007318, A007947, A098426.

Programs

Maple

A080396 := proc(n,k)
    A007947(binomial(n,k)) ;
end proc:
seq(seq( A080396(n,k),k=0..n),n=0..12) ; # R. J. Mathar, Mar 02 2025

PARI

T(n,k) = factorback(factorint(binomial(n,k))[, 1]);
tabl(nn) = for(n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print); \\ Michel Marcus, May 20 2018

Formula

T(n,k) = A007947(A007318(n,k)).

Row sums: sum_{k=0..n} T(n,k) = 2*A098426(n), n>0. - R. J. Mathar, Mar 02 2025