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

1,1

Links

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

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

Cf. A001222, A007318, A020738, A020733.

Sequence in context: A366770 A355249 A337618 * A364663 A101050 A128979

Adjacent sequences: A048682 A048683 A048684 * A048686 A048687 A048688

Keyword

nonn

Author

Labos Elemer

Status

approved