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A249442 a(n) is the smallest m such that binomial(n,m) is not squarefree, or a(n)=0, if there is no such m.

%I A249442 #31 Nov 11 2014 08:37:23
%S A249442 0,0,0,0,1,0,3,0,1,1,2,0,1,5,3,7,1,2,1,2,1,4,3,0,1,1,2,1,1,3,3,5,1,2,
%T A249442 3,4,1,2,3,4,1,2,3,8,1,1,2,21,1,1,1,2,1,4,1,2,1,2,3,6,1,6,3,1,1,2,3,4,
%U A249442 1,6,3,8,1,2,3,1,1,3,3,8,1,1,2,3,1,5,3
%N A249442 a(n) is the smallest m such that binomial(n,m) is not squarefree, or a(n)=0, if there is no such m.
%C A249442 The sequence gives the position of the first zero on row n (both starting from zero) in the triangular table A103447, and zero if there is no zero on that row. After a(0) = 0, A048278 gives the positions of seven other zeros in the sequence.
%C A249442 Records are 0,1,3,5,7,8,21,... (A249439) in positions 0,4,6,13,15,43,47,... (A249440).
%H A249442 Antti Karttunen, <a href="/A249442/b249442.txt">Table of n, a(n) for n = 0..10000</a>
%F A249442 Other identities:
%F A249442 A249716(n) = binomial(n, a(n)). [A249716(n) gives the corresponding minimal nonsquarefree binomial coefficient, or 1 when n is one of the terms of A048278].
%t A249442 Table[If[#>n,0,#]&[NestWhile[#+1&,1,SquareFreeQ[Binomial[n,#]]&]],{n,0,100}] (* _Peter J. C. Moses_, Nov 04 2014 *)
%o A249442 (PARI)
%o A249442 A249442(n) = { for(k=0,n\2,if(0==moebius(binomial(n,k)),return(k))); return(0); }
%o A249442 for(n=0, 10000, write("b249442.txt", n, " ", A249442(n)));
%o A249442 \\ _Antti Karttunen_, Nov 04 2014
%Y A249442 A249439 gives the record values, A249440 the positions where they occur for the first time.
%Y A249442 Cf. A005117, A007913, A048277, A048278, A103447, A249716, A249717, A249718.
%Y A249442 Differs from A249695 for the first time at n=9.
%K A249442 nonn
%O A249442 0,7
%A A249442 _Antti Karttunen_ and _Vladimir Shevelev_, Oct 28 2014
%E A249442 More terms from _Peter J. C. Moses_, Oct 28 2014