This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Sidney Cadot has authored 4 sequences.
a[n_] := Length@Select[Range[2^(n - 1) + 1, 2^n - 1, 2], Total[Last /@ FactorInteger[#]] ==2 &]Table[a[n],{n,0,25}]
There are 7 integers in the range from 1 to n=10 that can be factored using only the first k=2 primes 2 and 3: {1, 2, 3, 4, 6, 8, 9}. Hence, a(10, 2)=7.
The table begins
| k
| 1 2 3 4 5
----+--------------
1 | 1 1 1 1 1
2 | 2 2 2 2 2
3 | 2 3 3 3 3
4 | 3 4 4 4 4
5 | 3 4 5 5 5
n 6 | 3 5 6 6 6
7 | 3 5 6 7 7
8 | 4 6 7 8 8
9 | 4 7 8 9 9
10 | 4 7 9 10 10
a[n_, k_] := With[{pp = Times @@ Prime[Range[k]]}, Count[Map[FixedPoint[#/GCD[#, pp] &, #] &, Range[n]], 1]];
Table[a[n, k], {n, 1, 10}, {k, 1, 5}] // TableForm
For n=5, there are four integers less than 32 (i.e., 2^5) that are the product of two odd primes: {3*3, 3*5, 3*7, 5*5} = {9, 15, 21, 25}; hence, a(5)=4.
a[n_]:=Length@Select[Range[1, 2^n - 1, 2], Total[Last /@ FactorInteger[#]] == 2 &]
Table[a[n],{n,0,24}]
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