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A353026 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not appeared that is a multiple of the smallest prime factor with minimal exponent of a(n-1) (cf. A067695).

%I A353026 #16 Apr 18 2022 12:29:26
%S A353026 1,2,4,6,8,10,12,3,9,15,18,14,16,20,5,25,30,22,24,21,27,33,36,26,28,7,
%T A353026 35,40,45,50,32,34,38,42,44,11,55,60,39,48,51,54,46,52,13,65,70,56,49,
%U A353026 63,77,84,57,66,58,62,64,68,17,85,75,69,72,78,74,76,19,95,80,90,82,86,88,99,110
%N A353026 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not appeared that is a multiple of the smallest prime factor with minimal exponent of a(n-1) (cf. A067695).
%C A353026 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.
%H A353026 Michael De Vlieger, <a href="/A353026/b353026.txt">Table of n, a(n) for n = 1..10000</a>
%H A353026 Scott R. Shannon, <a href="/A353026/a353026.png">Image of the first 100000 terms</a>. The green line is y = n.
%e A353026 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.
%e A353026 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.
%t A353026 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 *)
%Y A353026 Cf. A067695, A352793, A064413.
%K A353026 nonn
%O A353026 1,2
%A A353026 _Scott R. Shannon_, Apr 18 2022