login
A048685
a(n) is the number of times the maximum value of Omega(binomial(n, k)) occurs in the n-th row of Pascal's triangle, where Omega(n) is the number of prime divisors of n counted with multiplicity (A001222).
1
2, 1, 2, 3, 2, 1, 4, 2, 6, 3, 4, 2, 2, 1, 2, 4, 4, 2, 8, 2, 2, 3, 8, 2, 2, 3, 2, 3, 2, 1, 2, 4, 2, 4, 8, 2, 2, 2, 12, 2, 6, 2, 2, 2, 2, 1, 2, 2, 2, 4, 8, 2, 4, 2, 4, 2, 2, 5, 4, 2, 4, 1, 18, 2, 8, 2, 2, 10, 8, 2, 2, 6, 2, 2, 2, 2, 4, 2, 10, 8, 4, 4, 2, 6, 2, 3, 2, 2, 4, 2, 2, 2, 2, 1, 2, 4, 4, 2, 4, 2, 4, 4
OFFSET
1,1
LINKS
EXAMPLE
For n = 19, the A001222 spectrum for binomial(n,k) is: {0, 1, 3, 3, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 3, 3, 1, 0}. The maximum arises 8 times, so a(19) = 8.
MATHEMATICA
a[n_] := Module[{row = Table[PrimeOmega[Binomial[n, k]], {k, 0, n}]}, Count[row, Max[row]]]; Array[a, 100] (* Amiram Eldar, Aug 13 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved