1,1

The number 289697407994 is the 47th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 123 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).

Anton Mosunov, Table of n, a(n) for n = 1..123

C. Pomerance, The first function and its iterates, A Celebration of the Work of R. L. Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge U. Press, to appear.

a(1) = 300629385430, because it is the smallest number whose sum of proper divisors is equal to 289697407994: 1 + 2 + 5 + 10 + 11 + 22 + 55 + 110 + 2732994413 + 5465988826 + 13664972065 + 27329944130 + 30062938543 + 60125877086 + 150314692715 = 289697407994.

Cf. A001065, A283156, A283157, A287233, A287238, A287251, A287262.

Sequence in context: A345864 A354070 A273936 * A172578 A172588 A172691

Adjacent sequences: A287244 A287245 A287246 * A287248 A287249 A287250

fini,full,nonn

Anton Mosunov, May 22 2017

approved