

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.


7



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, 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, 1, 6, 3, 8, 1, 2, 3, 1, 1, 3, 3, 8, 1, 1, 2, 3, 1, 5, 3
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OFFSET

0,7


COMMENTS

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.
Records are 0,1,3,5,7,8,21,... (A249439) in positions 0,4,6,13,15,43,47,... (A249440).


LINKS



FORMULA

Other identities:
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].


MATHEMATICA

Table[If[#>n, 0, #]&[NestWhile[#+1&, 1, SquareFreeQ[Binomial[n, #]]&]], {n, 0, 100}] (* Peter J. C. Moses, Nov 04 2014 *)


PROG

(PARI)
A249442(n) = { for(k=0, n\2, if(0==moebius(binomial(n, k)), return(k))); return(0); }
for(n=0, 10000, write("b249442.txt", n, " ", A249442(n)));


CROSSREFS

A249439 gives the record values, A249440 the positions where they occur for the first time.
Differs from A249695 for the first time at n=9.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



