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2..a(n) is the smallest range in which the most common value of omega(k) is n, where omega(k) is the number of prime divisors of k (A001221).
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%I #5 May 21 2016 14:21:52

%S 2,46,22196,7870163103377

%N 2..a(n) is the smallest range in which the most common value of omega(k) is n, where omega(k) is the number of prime divisors of k (A001221).

%e Among the numbers from 2 to a(2)=46 the most common value of omega is 2. Indeed, there are 21 numbers for which omega is 1 (primes or prime powers) and 22 for which omega is 2.

%t a[n_] := Block[{c1=0, c2=0, v, k=1}, While[c2<=c1, v=PrimeNu[++k]; If[v == n-1, c1++]; If[v == n, c2++]]; k]; Array[a, 3]

%Y Cf. A001221, A273381.

%K nonn,more

%O 1,1

%A _Giovanni Resta_, May 21 2016