A048273 Maximal number of distinct prime factors in binomial coefficients C(n,k) for k = 0,...,n.

0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 12, 13, 14, 14, 14, 14, 15, 15, 14, 14, 14, 15

Offset

0,5

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Example

If n = 51 and k runs from 0 to 51, then a maximum of 11 distinct prime factors arise, for k = 20, 21, 22, 23, 28, 29, 30, 31.

Mathematica

Table[Max[Table[b = Binomial[n, k]; If[b == 1, 0, Length[FactorInteger[b]]], {k, 0, n}]], {n, 0, 100}] (* T. D. Noe, Apr 03 2012 *)

Crossrefs

Cf. A001405, A034973, A001221, A048571.

Sequence in context: A073578 A087866 A061392 * A333535 A364678 A175387

Adjacent sequences: A048270 A048271 A048272 * A048274 A048275 A048276

Keyword

nonn

Author

Labos Elemer

Status

approved