A356431 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with both a(n-1) and the number of divisors of a(n-1).

1, 2, 4, 6, 8, 10, 12, 3, 18, 9, 15, 20, 14, 16, 30, 22, 24, 26, 28, 21, 36, 27, 42, 32, 34, 38, 40, 44, 33, 48, 45, 39, 52, 46, 50, 54, 56, 58, 60, 51, 66, 62, 64, 70, 68, 72, 57, 76, 74, 78, 80, 5, 90, 63, 69, 84, 75, 81, 105, 96, 82, 86, 88, 92, 94, 98, 100, 102, 104, 106, 108, 87, 114, 110

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers although it may take a large number of terms for the primes to appear, e.g., 17 has not occurred after 100000 terms. In the same range the only fixed points are the first two terms; it is likely no more exist although this is unknown.

Links

Table of n, a(n) for n=1..74.

Scott R. Shannon, Image of the first 100000 terms. The green line is y = n.

Example

a(8) = 3 as a(7) = 12 which has six divisors, and 3 is the smallest unused number that shares a factor with both 12 and 6.

Crossrefs

Cf. A356430, A356432, A000005, A354960, A348086.

Sequence in context: A096922 A241071 A353026 * A345444 A319807 A055954

Adjacent sequences: A356428 A356429 A356430 * A356432 A356433 A356434

Keyword

nonn

Author

Scott R. Shannon, Aug 07 2022

Status

approved