cp's OEIS Frontend

A249716 The least nonsquarefree number on row n of Pascal's triangle, or 1 if all the terms on that row are squarefree.

%I A249716 #12 Nov 05 2014 11:22:02
%S A249716 1,1,1,1,4,1,20,1,8,9,45,1,12,1287,364,6435,16,136,18,171,20,5985,
%T A249716 1540,1,24,25,325,27,28,3654,4060,169911,32,528,5984,52360,36,666,
%U A249716 8436,82251,40,820,11480,145008513,44,45,1035,12551759587422,48,49,50,1275,52,292825,54,1485,56,1596,30856,45057474,60,55525372,37820,63,64,2080
%N A249716 The least nonsquarefree number on row n of Pascal's triangle, or 1 if all the terms on that row are squarefree.
%C A249716 After a(0) = 1, A048278 gives the positions of seven other ones in the sequence.
%H A249716 Antti Karttunen, <a href="/A249716/b249716.txt">Table of n, a(n) for n = 0..10000</a>
%F A249716 a(n) = binomial(n, A249442(n)).
%e A249716            Binomial coefficients     First squarefree     a(n)
%e A249716                  A007318             occurs at index?      =
%e A249716 ----------------------------------------------------------------------------
%e A249716 Row 0                1               no squarefrees        1 (by definition)
%e A249716 Row 1              1   1             no squarefrees        1
%e A249716 Row 2            1   2   1           no squarefrees        1
%e A249716 Row 3          1   3   3   1         no squarefrees        1
%e A249716 Row 4        1   4   6   4   1              1              4
%e A249716 Row 5      1   5  10  10   5   1     no squarefrees        1
%e A249716 Row 6    1   6  15  20  15   6   1          3             20
%o A249716 (PARI)
%o A249716 A249716(n) = { my(b); for(k=0,n\2,if(0==moebius(b=binomial(n,k)),return(b))); return(1); }
%o A249716 for(n=0, 10000, write("b249716.txt", n, " ", A249716(n)));
%o A249716 (Scheme) (define (A249716 n) (A007318tr n (A249442 n)))
%Y A249716 A249717 and A249718 give the smallest and the largest prime whose square divides these numbers.
%Y A249716 Cf. also A007318, A005117, A013929, A048277, A048278, A249442.
%K A249716 nonn
%O A249716 0,5
%A A249716 _Antti Karttunen_, Nov 04 2014