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

1,1

Comments

Proper subset of A369361.

Superset of A368089.

Links

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

Formula

{a(n)} = A126706 \ A025487.

Example

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.

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[#]} &]

Crossrefs

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

Sequence in context: A255848 A072904 A268284 * A054279 A186781 A164711

Adjacent sequences: A367265 A367266 A367267 * A367269 A367270 A367271

Keyword

nonn

Author

Michael De Vlieger, Jan 28 2024

Status

approved