A367268 Numbers k that are not squarefree, not prime powers, and not products of primorials.

18, 20, 28, 40, 44, 45, 50, 52, 54, 56, 63, 68, 75, 76, 80, 84, 88, 90, 92, 98, 99, 100, 104, 108, 112, 116, 117, 124, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 184, 188, 189, 196, 198, 200, 204, 207, 208, 212

Offset: 1

Author

Michael De Vlieger, Jan 28 2024

Keywords

• nonn

Comments

Proper subset of A369361.

Superset of A368089.

Examples

			Let P(n) = A002110(n).
12 = 6 * 2 = P(2) * P(1) is not in this sequence.
a(1) = 18 = 6 * 3 is not a product of primorials.
a(2) = 20 = 2 * 2 * 5 is not a product of primorials, etc.
		

Links

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

Crossrefs

Cf. A000961, A002110, A005117, A013929, A024619, A025487, A126706, A368089, A369361.

Programs

Mathematica

Select[Select[Range[5000], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], Nand[EvenQ[#1], Union@ Differences@ PrimePi[#2[[All, 1]]] == {1}, AllTrue[Differences@ #2[[All, -1]], # <= 0 &]] & @@ {#, FactorInteger[#]} &]

Formula

{a(n)} = A126706 \ A025487.