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Amiram Eldar, <a href="/A342012/b342012.txt">Table of n, a(n) for n = 1..10000</a>

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In contrast to A329902, this sequence is monotonic. Proof: , because each term is obtained from the previous, either by multiplying it by 2, or by "bumping" one [or hypothetically: two] of its prime factors one step up (i.e., replacing it with the next larger prime). Both , and both operations are guaranteed to make the number larger, therefore each term is strictly larger than the previous.

In contrast to A329902, this sequence is monotonic. Proof: each term is obtained from the previous, either by multiplying it by 2, or by "bumping" one [or hypothetically: two] of its prime factors one step up (i.e., replacing it with the next larger prime). Both steps operations are guaranteed to increase make the number, therefor larger, therefore each term is strictly larger than the previous.

\\ Or alternatively, using:

A329900(n) = { my(m=1, pp=1); while(1, forprime(p=2, , if(n%p, if(2==p, return(m), break), n /= p; pp = p)); m *= pp); (m); };

A342012(n) = A329900(A004490(n));

In contrast to A329902, this sequence is monotonic. Proof: each term is obtained from the previous, either by multiplying it by 2, or by "bumping" one [or hypothetically: two] of its prime factors one step up (i.e., replacing it with the next larger prime). Both steps are guaranteed to grow increase the number, therefor each term is strictly larger than the previous.

Cf. also A217867, A329902.

In contrast to A329902, this sequence is monotonic. Proof: each term is obtained from the previous, either by multiplying it by 2, or by "bumping" one [or hypothetically: two] of its prime factors one step up (i.e., replacing it with the next larger prime). Both steps are guaranteed to grow the number, therefor each term is strictly larger than the previous.