OFFSET
1,2
COMMENTS
The sequences is conjectured to be a permutation of the positive integers. In the first 500000 terms any time a prime p appears, where p>=5, the following term is 5p. It is unknown if this is true for all primes. In the same range the fixed points are 1, 2, 9, 39, 49, 1079, 4897, although it is possible more exist.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Scott R. Shannon, Image of the first 100000 terms. The green line is y = n.
EXAMPLE
a(4) = 6 as a(3) = 4 = 2*2 which has A067695(4) = 2 as the smallest prime factor with minimal exponent, and 6 is the smallest unused number that is a multiple of 2.
a(8) = 3 as a(7) = 12 = 2*2*3 which has A067695(12) = 3 as the smallest prime factor with minimal exponent, and 3 is the smallest unused number that is a multiple of 3.
MATHEMATICA
nn = 75, c[_] = 0; Array[Set[{a[#], c[#]}, {#, #}] &, 2]; u = 3; Do[p = MinimalBy[FactorInteger@ a[i - 1], Last][[1, 1]]; k = u; While[Nand[c[k] == 0, Divisible[k, p]], k++]; Set[{a[i], c[k]}, {k, i}]; If[k == u, While[c[u] > 0, u++]], {i, Length[s] + 1, nn}]; Array[a, nn] (* Michael De Vlieger, Apr 18 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Apr 18 2022
STATUS
approved