A368089 Numbers k neither squarefree nor prime powers whose squarefree kernel is not a primorial.

20, 28, 40, 44, 45, 50, 52, 56, 63, 68, 75, 76, 80, 84, 88, 92, 98, 99, 100, 104, 112, 116, 117, 124, 126, 132, 135, 136, 140, 147, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 184, 188, 189, 196, 198, 200, 204, 207, 208, 212, 220, 224, 225, 228, 232

Offset: 1

Author

Michael De Vlieger, Jan 20 2024

Keywords

• nonn

Comments

Numbers k such that Omega(k) > omega(k) > 1 such that squarefree kernel rad(k) is not in A002110, where Omega = A001222, omega = A001221, and rad(k) = A007947(k).

Contains numbers k in A126706 that are not of the form m*P(n), where P(n) = A002110(n), rad(m) | P(n), m > 1, n > 1.

Links

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

Crossrefs

Cf. A001221, A001222, A002110, A007947, A055932, A126706, A367268.

Programs

Mathematica

Select[Select[Range[240], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], Nand[EvenQ[#], Union@ Differences@ PrimePi[FactorInteger[#][[All, 1]]] == {1}] &]

Formula

This sequence is { A126706 \ A055932 } = { A126706 \ A367268 }.