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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).

%I A379548 #15 Dec 28 2024 18:21:21
%S A379548 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,
%T A379548 55,70,69,74,78,65,82,87,86,93,94,102,85,106,105,110,111,114,95,118,
%U A379548 123,122,129,130,138,115,134,141,142,159,146,165,154,174,145,158
%N 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).
%C A379548 Squarefree version of A351495, conjectured to be a permutation of the squarefree numbers, A005117.
%H A379548 Michael De Vlieger, <a href="/A379548/b379548.txt">Table of n, a(n) for n = 1..10000</a>
%e A379548 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.
%t A379548 nn = 120; c[_] := False; s = {1}; m[_] := 1; j = 1; c[1] = True;
%t A379548 f[x_] := Block[{q = 2}, While[Divisible[x, q], q = NextPrime[q]]; q];
%t A379548 {j}~Join~Reap[Monitor[Do[k = f[j];
%t A379548   While[Or[c[k*m[k]], ! SquareFreeQ[k*m[k]]], m[k]++];
%t A379548 k *= m[k]; j = Sow[k]; c[k] = True, {n, 2, nn}], n] ][[-1, 1]] (* _Michael De Vlieger_, Dec 28 2024 *)
%Y A379548 Cf. A005117, A351495.
%K A379548 nonn
%O A379548 1,2
%A A379548 _David James Sycamore_, Dec 25 2024
%E A379548 More terms from _Jinyuan Wang_, Dec 25 2024