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

0,5

Links

Table of n, a(n) for n=0..80.

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

Example

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, ...

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

Prog

(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

Crossrefs

Cf. A007318, A007947, A098426.

Sequence in context: A307239 A204087 A080381 * A155582 A169946 A160832

Adjacent sequences: A080393 A080394 A080395 * A080397 A080398 A080399

Keyword

nonn,tabl

Author

Labos Elemer, Mar 19 2003

Status

approved