A273381 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 factors of k (A001222).
2, 26, 15526, 151165506068
Offset: 1
Examples
Among the numbers from 2 to a(2)=26 the most common value of Omega is 2. Indeed, there are 9 numbers for which Omega is 1 (the primes) and 10 for which Omega is 2 (the semiprimes).
Programs
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Mathematica
a[n_] := Block[{c1=0, c2=0, v, k=1}, While[c2<=c1, v=PrimeOmega[++k]; If[v == n-1, c1++]; If[v == n, c2++]]; k]; Array[a, 3]