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A020733 Consider number of prime divisors of C(n,k), k=0..n; a(n) = multiplicity of maximal value. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)