OFFSET
1,2
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Scatterplot of a(n), n = 1..2^20.
Michael De Vlieger, Log-log scatterplot of a(n), n = 1..2^14, showing records in red, local minima in blue, highlighting primes in green and other prime powers in gold.
EXAMPLE
a(1) = 1, a(2) = 2 and 2 divides 2 but does not divide 1. Since 2 is the only prime divisor of 2, a(3) = 4, the smallest unused multiple of 2.
Since every prime divisor of a(3)=4 also divides a(2) = 2, a(4) = 6, the least novel multiple of the squarefree kernel of 4.
a(19,20) = (25,30); 2|30 and 3|30 but 2 and 3 do not divide 25. The smallest multiple of 2*3 = 6 not already in the sequence is 36. Therefore a(21) = 36.
MATHEMATICA
nn = 67; c[_] = False; q[_] = 1; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; q[2] = 2; Do[m = FactorInteger[a[n - 1]][[All, 1]]; If[Length@ # == 0, While[Set[k, #* q[#]]; c[k], q[#]++] &[Times @@ m], While[Set[k, #* q[#]]; c[k], q[#]++] &[Times @@ #]] &@ Select[m, CoprimeQ[#, a[n - 2]] &]; Set[{a[n], c[k]}, {k, True}], {n, 3, nn}]; Array[a, nn]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Oct 22 2022
STATUS
approved