A379548 a(1) = 1. For n > 1, a(n) is the earliest novel squarefree number divisible by the smallest prime which does not divide a(n-1).

1, 2, 3, 6, 5, 10, 15, 14, 21, 22, 30, 7, 26, 33, 34, 39, 38, 42, 35, 46, 51, 58, 57, 62, 66, 55, 70, 69, 74, 78, 65, 82, 87, 86, 93, 94, 102, 85, 106, 105, 110, 111, 114, 95, 118, 123, 122, 129, 130, 138, 115, 134, 141, 142, 159, 146, 165, 154, 174, 145, 158

Offset: 1

Author

David James Sycamore, Dec 25 2024

Keywords

• nonn

Comments

Squarefree version of A351495, conjectured to be a permutation of the squarefree numbers, A005117.

Examples

			a(1)=1 implies a(2)=2, the smallest novel squarefree number divisible by 2, the least non divisor prime of 1. Likewise a(3)=3. a(4) must be the smallest squarefree multiple of 2, the least non divisor prime of 3, so a(4) cannot be 4, it must be 6 which is squarefree.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A351495.

Programs

Mathematica

nn = 120; c[] := False; s = {1}; m[] := 1; j = 1; c[1] = True;
f[x_] := Block[{q = 2}, While[Divisible[x, q], q = NextPrime[q]]; q];
{j}~Join~Reap[Monitor[Do[k = f[j];
  While[Or[c[k*m[k]], ! SquareFreeQ[k*m[k]]], m[k]++];
k *= m[k]; j = Sow[k]; c[k] = True, {n, 2, nn}], n] ][[-1, 1]] (* Michael De Vlieger, Dec 28 2024 *)

Extensions

More terms from Jinyuan Wang, Dec 25 2024