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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).

%I A048685 #13 Aug 13 2024 05:34:25
%S A048685 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,
%T A048685 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,
%U A048685 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
%N 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).
%H A048685 Amiram Eldar, <a href="/A048685/b048685.txt">Table of n, a(n) for n = 1..10000</a>
%e A048685 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.
%t A048685 a[n_] := Module[{row = Table[PrimeOmega[Binomial[n, k]], {k, 0, n}]}, Count[row, Max[row]]]; Array[a, 100] (* _Amiram Eldar_, Aug 13 2024 *)
%Y A048685 Cf. A001222, A007318, A020738, A020733.
%K A048685 nonn
%O A048685 1,1
%A A048685 _Labos Elemer_