This is the sequence of prime numbers which are the elementary building blocks for the superior highly composite numbers:
$2, 3, 2, 5, 2, 3, 7, 2, 11, 13, 2, 3, 5, 17, 19, 2, 23, 7, 29, 3, 31, 2, 37, 41, 43, 47, ...$
The $n^{th}$ superior highly composite number is the product of the first $n$ primes in this sequence.
To generate this sequence we need to calculate $$\frac{\log \left(1 + \frac{1}{\epsilon} \right)}{\log p}. $$ for many values of the prime $p$ and the exponent $\epsilon$.
Print these values out and sort them in decreasing order. And we obtain the sequence in question.
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This is the sequence of prime numbers which are the elementary building blocks for the colossally abundant numbers:
$2, 3, 2, 5, 2, 3, 7, 2, 11, 13, 2, 3, 5, 17, 19, 23, 2, 29, 31, 7, 3, 37, 41, 43, 2, ...$
The $n^{th}$ colossally abundant number is the product of the first $n$ primes in this sequence.
Notice that the first $15$ terms in this second sequence are the exact same as the first $15$ terms in the first sequence. But after the first $15$ terms the two sequences are different.
My question is: how can we generate this second sequence of primes?