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

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, 33, 36, 39, 38, 7, 40, 42, 44, 45, 46, 50, 48, 51, 52, 54, 56, 55, 58, 57, 60, 63, 62, 65, 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

Offset: 1

Author

Scott R. Shannon, Jan 18 2024

Keywords

• nonn

Comments

The sequence is conjectured to be a permutation of the positive integers.

The empty product 1 never appears - Michael De Vlieger, Jan 24 2024

Examples

			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.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A369272, A351495, A053669, A002110.

Programs

Mathematica

nn = 2^10;
c[] := False; m[] := 1;
f[x_] := Block[{q = 2}, While[Divisible[x, q], q = NextPrime[q]]; q];
Do[While[c[Set[k, #*m[#]]], m[#]++] &[f[i]];
  Set[{a[i], c[k]}, {k, True}], {i, nn}];
Array[a, nn] (* Michael De Vlieger, Jan 24 2024 *)

Formula

a(A002110(k-1)) = the k-th prime.