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I have a series of 30 given numbers as given : $0, 2, 4, 5, 6, 7, 7, 9, 8, 8, 9, 13, 9, 15, 11, 10, 10, 19, 10, 21, 11, 12, 15, 25, 11, 12, 17, 11, 13, 31$ and $12$.

This was generated by the following method :

First I took all even numbers upto 60, starting from 0.
Then, I took out all its prime factors. Prime factors that were repeated were treated as explicit factors.
Then I added all prime factors (of each even number) up (including repeating ones) and wrote them alongside.

This formed a series of numbers as given in the top. This (pattern?) should somehow depend on the pattern of prime numbers. Is it possible to write a mathematical function for generating the nth number of this series ?

Super Coder
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    There is no way to answer your question with so little information. If you [edit] the question to tell us where this sequence comes from and how you found the first $30$ terms we may be able to help. – Ethan Bolker Jun 07 '23 at 20:05
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    One can can construct arbitrarily many patterns with arbitrarily many different answers, these questions are not math. – kodiak Jun 07 '23 at 20:08
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    The OEIS suggests only one plausible match (link), at least for those sequences of interest within its database. Of course, as stated, it is entirely plausible that the pattern is different altogether, because a sequence sans context is entirely meaningless. – PrincessEev Jun 07 '23 at 20:15
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    From the question, the next number after the first $30$ given numbers is $12$. – peterwhy Jun 07 '23 at 20:18
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    @peter, $8=2\times2\times2$, and $2+2+2=8$. $12=2\times2\times3$, and $2+2+3=7$. $n$ maps to the sum of the prime divisors on $n$, taken with multiplicity. – Gerry Myerson Jun 11 '23 at 03:13

1 Answers1

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If you don't restrict to even numbers, you get https://oeis.org/A001414 and you will find there are many references and links at that site. No "mathematical function" is given (although that depends on what exactly you mean by that phrase). If the prime factorization of $n$ is $n=p_1^{a_1}p_2^{a_2}\dotsb p_r^{a_r}$, then your function is $\sum_{j=1}^ra_jp_j$

Gerry Myerson
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