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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. 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 (list; graph; refs; listen; history; text; internal format)
 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 Antti Karttunen, Table of n, a(n) for n = 0..10000 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))); \\ Antti Karttunen, Nov 04 2014 CROSSREFS A249439 gives the record values, A249440 the positions where they occur for the first time. Cf. A005117, A007913, A048277, A048278, A103447, A249716, A249717, A249718. Differs from A249695 for the first time at n=9. Sequence in context: A239264 A294289 A059341 * A334739 A131802 A069023 Adjacent sequences: A249439 A249440 A249441 * A249443 A249444 A249445 KEYWORD nonn AUTHOR Antti Karttunen and Vladimir Shevelev, Oct 28 2014 EXTENSIONS More terms from Peter J. C. Moses, Oct 28 2014 STATUS approved

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Last modified June 17 18:36 EDT 2024. Contains 373463 sequences. (Running on oeis4.)