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A369271 The smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide n.

%I A369271 #11 Jan 24 2024 08:29:24
%S A369271 2,3,4,6,8,5,10,9,12,15,14,20,16,18,22,21,24,25,26,27,28,30,32,35,34,
%T A369271 33,36,39,38,7,40,42,44,45,46,50,48,51,52,54,56,55,58,57,60,63,62,65,
%U A369271 64,66,68,69,70,75,72,78,74,81,76,49,80,84,82,87,86,85,88,90,92,93,94,95,96,99,98
%N A369271 The smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide n.
%C A369271 The sequence is conjectured to be a permutation of the positive integers.
%C A369271 The empty product 1 never appears - _Michael De Vlieger_, Jan 24 2024
%H A369271 Scott R. Shannon, <a href="/A369271/b369271.txt">Table of n, a(n) for n = 1..10000</a>
%F A369271 a(A002110(k-1)) = the k-th prime.
%e A369271 a(7) = 10 as 2 is the smallest prime that does not divide 7, and 10 = 2*5 is the smallest multiple of 2 that has not yet appeared.
%t A369271 nn = 2^10;
%t A369271 c[_] := False; m[_] := 1;
%t A369271 f[x_] := Block[{q = 2}, While[Divisible[x, q], q = NextPrime[q]]; q];
%t A369271 Do[While[c[Set[k, #*m[#]]], m[#]++] &[f[i]];
%t A369271   Set[{a[i], c[k]}, {k, True}], {i, nn}];
%t A369271 Array[a, nn] (* _Michael De Vlieger_, Jan 24 2024 *)
%Y A369271 Cf. A369272, A351495, A053669, A002110.
%K A369271 nonn
%O A369271 1,1
%A A369271 _Scott R. Shannon_, Jan 18 2024