A362684 a(n) is the index at which n first occurs in A362681.

1, 3, 5, 7, 26, 49, 632, 1682

Offset: 0

Author

Kevin L. Schwartz and Christian N. K. Anderson, May 01 2023

Keywords

• nonn
• hard
• more

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

Examples

			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

Cf. A362681, A157449.

Cf. A048133.

Extensions

a(0)=1 prepended by Michel Marcus, Oct 11 2023