A356430 - OEIS

A356430

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

1, 2, 4, 3, 6, 8, 10, 12, 9, 15, 14, 16, 5, 18, 20, 21, 22, 24, 26, 28, 27, 30, 32, 33, 34, 36, 39, 38, 40, 42, 44, 45, 46, 48, 25, 51, 50, 52, 54, 56, 58, 60, 57, 62, 64, 7, 66, 68, 63, 69, 70, 72, 74, 76, 75, 78, 80, 35, 82, 84, 81, 55, 86, 88, 90, 87, 92, 93, 94, 96, 98, 99, 100, 102, 104

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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., 19 has not occurred after 100000 terms. In the same range the only fixed points are 1, 2, and 9, and it is likely no more exist.

LINKS

Table of n, a(n) for n=1..75.

Scott R. Shannon, Image of the first 1000 terms. The green line is y = n.

EXAMPLE

a(9) = 9 as a(8) = 12 which has six divisors, and 9 is the smallest unused number that shares a factor with 6.

CROSSREFS

Cf. A356431, A356432, A000005, A354960, A348086.

Sequence in context: A352714 A355435 A155487 * A128555 A039874 A193991

Adjacent sequences: A356427 A356428 A356429 * A356431 A356432 A356433

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Aug 07 2022

STATUS

approved