A395132 a(n) = smallest integer k > 1 such that A394453(k) = n, or -1 if no such k exists.

3, 2, 13, 9, 18, 10, 20, 19, 27, 54, 34, 74, 73, 109, 106, 93, 50, 100, 200, 199, 343, 513, 872, 794, 1078, 1129, 1228, 867, 1734, 976, 1153, 1461, 2922, 4612, 5843, 18448, 17529, 23372, 23371, 36962, 70113, 104882, 210682, 258733, 681327, 776199, 1328044, 1678108, 2365562

Offset

0,1

Comments

The iteration function f is defined in A394453: if sigma(n) < 2*n then f(n) = sigma(n), else f(n) = n / spf(n), where spf(n) is the smallest prime factor. All terms are based on empirical verification up to 10^9; beyond that, larger terms may exist. If some step count never occurs, the corresponding term would be -1.

Links

Lu Zhuofan, Table of n, a(n) for n = 0..62

Zhuofan Lu, Two Attractors in an Iteration System Based on the Sum of Proper Divisors and the Smallest Prime Factor, figshare, preprint, 2026.

Example

a(0) = 3 because A394453(3) = 0 (3 is in the cycle C0).
a(1) = 2 because A394453(2) = 1 (2 -> 3, which is in C0).
a(2) = 13 because A394453(13) = 2 (13 -> 14 -> 24, which is in C0).

Crossrefs

Cf. A394453 (iteration steps), A000203 (sigma), A005100 (deficient), A020639 (smallest prime factor).

Sequence in context: A191705 A252669 A131050 * A219374 A084416 A210604

Adjacent sequences: A395129 A395130 A395131 * A395133 A395134 A395135

Keyword

nonn

Author

Lu Zhuofan, Apr 12 2026

Status

approved