login
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).
7
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
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
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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Aug 07 2022
STATUS
approved