|
Search: id:A048278
|
|
|
| A048278 |
|
Numbers n such that the numbers binomial(n,k) are square-free (or 1) for all k = 0..n. |
|
+0
2
|
| |
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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]
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
A. Granville and O. Ramar\'e, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika 43 (1996), 73-107.
|
|
EXAMPLE
|
n=11: C[11,k] = 1,11,55,165,330,462,... are all square-free (or 1).
|
|
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]} ]
|
|
CROSSREFS
|
Cf. A005117, A046098, A048276, A048277, A048279.
Sequence in context: A075049 A061165 A046689 this_sequence A068863 A087521 A078403
Adjacent sequences: A048275 A048276 A048277 this_sequence A048279 A048280 A048281
|
|
KEYWORD
|
nonn,fini,full
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu)
|
|
EXTENSIONS
|
Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 03 2004
|
|
|
Search completed in 0.002 seconds
|
