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 A367268 Numbers k that are not squarefree, not prime powers, and not products of primorials. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)