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).

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

Author

Labos Elemer

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A007318, A020738, A020733.

Programs

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 *)