Sequence summation chains

Russell Walsmith ixitol at gmail.com
Thu Jul 20 09:18:42 CEST 2006

```The "sopf" (sum of prime factors) function
(A001414<http://www.research.att.com/%7Enjas/sequences/A001414>)
downgrades the operators in a prime decomposition. E.g., 40 factors as 2^3 *
5 and sopf(40) = 2 * 3 + 5 =11. Iteration of sopf gives the sequences
A002217 <http://www.research.att.com/%7Enjas/sequences/A002217> and
A029908<http://www.research.att.com/%7Enjas/sequences/A029908>.
(it would be nice to have these transforms in the OEIS library BTW.)

http://www.research.att.com/~njas/sequences/transforms.html

An extension of this idea is to sum iterations of sopf(n) and add to n to
generate n[2], halting finally when n[j] is prime. This gives the sequences

1, 1, 1, 1, 2, 1, 2, 6, 2, 1, 2, 1, 3, 3, 6, 1, 2, 1, 5, 31, 6

2, 3, 4, 5, 11, 7, 19, 131, 17, 11, 19, 13, 53, 53, 137, 17, 37, 19, 131,
5237, 137
which I'll soon submit as *A120978 and A120979 respectively. I have more
terms, but it was very tedious to calculate them and I'm not certain of
their accuracy. If anyone sees a way to automate the process, lemme know.