Generate a mathematical sequence of real numbers in Maxima

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I need to perform a function that calculates the $n$th term of the next succession:

$1, 6, 16, 37, 63, 113, 163, 248, 339, 469, 591, 801, 971, 1221$...

For more information about the succession, I leave you this link.

I have tried to do it with the following code:

succession(n) :=
 sum(divsum(k,2), k, 1, n)$

For small numbers, such as six or seven, it works. But, the problem is that they ask me to make the program able to compile the following cases:

succession(10^17)

succession(12^24)

I have already raised this question in stackOverflow, but many have recommended I post it here.

Thanks.