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A048278
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Numbers n such that the numbers binomial(n,k) are squarefree (or 1) for all k = 0..n.
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1
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OFFSET
| 1,2
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COMMENTS
| It has been shown by Granville and Ramar\'e that the sequence is complete.
These are all the positive integers m that, when m is represented in binary, contain no composites represented in binary as substrings. [From Leroy Quet Oct 30 2008]
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LINKS
| A. Granville and O. Ramar\'e, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43 (1996), 73-107.
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EXAMPLE
| n=11: C[11,k] = 1,11,55,165,330,462,... are all squarefree (or 1).
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MATHEMATICA
| Do[m = Prime[n]; k = 2; While[k < m/2 + .5 && Union[ Transpose[ FactorInteger[ Binomial[m, k]]] [[2]]] [[ -1]] < 2, k++ ]; If[k >= m/2 + .5, Print[ Prime[n]]], {n, 1, PrimePi[10^6]} ]
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CROSSREFS
| Cf. A005117, A046098, A048276, A048277, A048279.
Sequence in context: A061165 A183055 A046689 * A068863 A087521 A078403
Adjacent sequences: A048275 A048276 A048277 * A048279 A048280 A048281
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KEYWORD
| nonn,fini,full
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 03 2004
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