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My friend John asked me what is the next number in the sequence $$1,4,8,16,17,44,58,76,\dots ?$$ I told him it could be anything, and I asked for a clue. He told me it involves adding numbers that have no prime factor in it more than once like $4$ or $12$ because they have a factor of the prime $2$ twice.

I’m asking for possible solutions to this puzzle not for a definite answer. I tried to look this series up on the oeis but it didn’t show up there.

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1 Answer 1

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I think I have an idea for a possible way he got the sequence. he could have added rows of this triangle

1

2,2

3,2,3

2,6,6,2

5,2,3,2,5

…

where its the triangle of the multiplication table but if it has an extra prime factor than it’s prime factor is taken off.

1

2,2

3,4,3

4,6,6,4

5,8,9,8,5

…

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  • $\begingroup$ How in god’s name did you think of this so quickly lmao. It would have been eight hours before I considered the anti-diagonals of the multiplication table of $\Bbb N$ $\endgroup$
    – pancini
    Commented Jun 2, 2021 at 2:09
  • $\begingroup$ First of all please refer EOQS as well as type the math using mathjax $\endgroup$
    – user876009
    Commented Jun 2, 2021 at 2:12