A020733 Consider number of prime divisors of binomial(n,k), k=0..n; a(n) = multiplicity of the maximum 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

Author

Labos Elemer

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Robert Israel)

Crossrefs

Cf. A001221, A048484, A048486.

Programs

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 *)

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