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