OFFSET
0,2
COMMENTS
Among terms n=1..7, each number iterates through the previous terms. For example, the first iteration takes 1682 to 632=a(6), the second takes 632 to 49=a(5) and so forth.
1682 is the only number < 10^6 that requires 7 iterations to reach completion.
a(8), if it exists, is larger than 10^6.
a(8) > 10^9. - Michel Marcus, Oct 11 2023
EXAMPLE
a(7) = 1682 because the first number to require 7 iterations to reach 2 or less is 1682.
Each iteration step is n <- 2n - {sum of proper factors of 2n} = A157449(2n); for n = 1682, this gives 2n = 3364, 3364 - (2 + 4 + 29 + 58 + 116 + 841 + 1682) = 632, which is a(6).
Note that the proper factors of x are all divisors of x other than 1 and x.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Kevin L. Schwartz and Christian N. K. Anderson, May 01 2023
EXTENSIONS
a(0)=1 prepended by Michel Marcus, Oct 11 2023
STATUS
approved