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

%I A080396 #16 Mar 02 2025 07:58:04
%S A080396 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,
%T A080396 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,
%U A080396 30,210,42,210,30,15,10,1,1,11,55,165,330,462,462,330,165,55,11,1,1,6,66
%N A080396 Largest squarefree numbers dividing the binomial coefficients C(n,k) read by row, 0<=k<=n. Squarefree kernel of Pascal triangle.
%F A080396 T(n,k) = A007947(A007318(n,k)).
%F A080396 Row sums: sum_{k=0..n} T(n,k) = 2*A098426(n), n>0. - _R. J. Mathar_, Mar 02 2025
%e A080396 Triangle begins:
%e A080396 1,
%e A080396 1,1,
%e A080396 1,2,1,
%e A080396 1,3,3,1,
%e A080396 1,2,6,2,1,
%e A080396 1,5,10,10,5,1,
%e A080396 1,6,15,10,15,6,1, ...
%p A080396 A080396 := proc(n,k)
%p A080396     A007947(binomial(n,k)) ;
%p A080396 end proc:
%p A080396 seq(seq( A080396(n,k),k=0..n),n=0..12) ; # _R. J. Mathar_, Mar 02 2025
%o A080396 (PARI) T(n,k) = factorback(factorint(binomial(n,k))[, 1]);
%o A080396 tabl(nn) = for(n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, May 20 2018
%Y A080396 Cf. A007318, A007947, A098426.
%K A080396 nonn,tabl
%O A080396 0,5
%A A080396 _Labos Elemer_, Mar 19 2003