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A020738
Consider number of divisors of binomial(n, k), k=0..n; a(n) = multiplicity of the maximum value.
3
2, 1, 2, 1, 2, 1, 4, 3, 4, 1, 4, 3, 2, 1, 2, 1, 6, 2, 6, 2, 6, 1, 8, 2, 2, 1, 4, 2, 2, 1, 10, 4, 2, 5, 2, 2, 2, 1, 2, 1, 6, 2, 2, 2, 4, 1, 2, 1, 2, 2, 6, 2, 4, 2, 2, 4, 2, 1, 10, 2, 2, 3, 4, 8, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 6, 2, 2, 2, 12, 2, 2, 1, 2, 4, 4, 2, 2, 2, 2, 1, 2, 2, 2, 1, 4, 2, 4, 2
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)
EXAMPLE
If n = 23, the numbers of divisors of {binomial(23, k)} are {1, 2, 4, 8, 16, 16, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 32, ...}. The maximum occurs 8 times, so a(23) = 8.
MAPLE
f:= proc(n) local L, k;
L:= [seq(numtheory:-tau(binomial(n, k)), k=0..n)];
numboccur(max(L), L)
end proc:
map(f, [$1..200]); # Robert Israel, Nov 17 2016
MATHEMATICA
a[ n_] := If[ n < 1, 0, Last @ Last @ Tally @ Array[ Length @ Divisors @ Binomial[n, #] &, n+1, 0]]; (* Michael Somos, Nov 17 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved