A020733 Consider number of prime divisors of C(n,k), k=0..n; a(n) = multiplicity of maximal value.

2, 1, 2, 1, 2, 5, 4, 1, 4, 2, 4, 1, 2, 5, 8, 1, 2, 5, 8, 2, 6, 7, 8, 5, 8, 11, 2, 2, 4, 11, 10, 3, 8, 2, 6, 3, 6, 2, 4, 1, 2, 5, 8, 2, 12, 16, 16, 5, 6, 13, 8, 12, 12, 4, 8, 5, 4, 5, 6, 4, 2, 6, 10, 1, 2, 7, 6, 5, 2, 2, 12, 15, 16, 2, 8, 11, 2, 10, 10, 11, 2, 6, 12, 3, 16, 2, 4, 8, 10, 5, 2, 2, 4, 6

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

The number of distinct primes of C(15,k) are {0,2,3,3,4,4,4,4,4,4,4,4,3,3,2,0}; maximum is 4 and occurs 8 times; thus a(15)=8.

Maple

f:= proc(n) local A, i;
  A:= [seq(nops(numtheory:-factorset(binomial(n, i))), i=0..n)];
  numboccur(max(A), A);
end proc:
map(f, [$1..100]); # Robert Israel, May 26 2020

Mathematica

a[n_] := Sort[Tally[Table[PrimeNu[Binomial[n, k]], {k, 0, n}]]][[-1, 2]];
Array[a, 100] (* Jean-François Alcover, Jun 09 2020 *)

Prog

(PARI) a(n) = {v = vector(n+1, k, omega(binomial(n, k-1))); m = vecmax(v); sum(i=1, n+1, v[i] == m); } \\ Michel Marcus, Dec 30 2013

Crossrefs

Cf. A001221, A048484, A048486.

Sequence in context: A050325 A332510 A001314 * A210700 A215745 A059913

Adjacent sequences: A020730 A020731 A020732 * A020734 A020735 A020736

Keyword

nonn

Author

Labos Elemer

Status

approved