|
%I #35 Oct 11 2023 08:43:26
%S 1,3,5,7,26,49,632,1682
%N a(n) is the index at which n first occurs in A362681.
%C 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.
%C 1682 is the only number < 10^6 that requires 7 iterations to reach completion.
%C a(8), if it exists, is larger than 10^6.
%C a(8) > 10^9. - _Michel Marcus_, Oct 11 2023
%e a(7) = 1682 because the first number to require 7 iterations to reach 2 or less is 1682.
%e 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).
%e Note that the proper factors of x are all divisors of x other than 1 and x.
%Y Cf. A362681, A157449.
%Y Cf. A048133.
%K nonn,hard,more
%O 0,2
%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 01 2023
%E a(0)=1 prepended by _Michel Marcus_, Oct 11 2023
| 