A387919 - OEIS

A387919

Numbers k that are neither squarefree, nor squareful, nor a product of primorials.

18, 20, 28, 40, 44, 45, 50, 52, 54, 56, 63, 68, 75, 76, 80, 84, 88, 90, 92, 98, 99, 104, 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, 198, 204, 207, 208, 212, 220, 224, 228, 232

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OFFSET

1,1

COMMENTS

A369361 is the union of this sequence and A369636.

Intersection of A332785 and A369361 = A332785 \ A025487.

LINKS

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

EXAMPLE

n a(n)

-------------------

1 18 = 2 * 3^2

2 20 = 2^2 * 5

3 28 = 2^2 * 7

4 40 = 2^3 * 5

5 44 = 2^2 * 11

6 45 = 3^2 * 5

7 50 = 2 * 5^2

8 52 = 2^2 * 13

9 54 = 2 * 3^3

10 56 = 2^3 * 7

11 63 = 3^2 * 7

12 68 = 2^2 * 17

MATHEMATICA

fQ[x_] := And[Nor[PrimePowerQ[x], SquareFreeQ[x]], Min[#] == 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, ReverseSort[#]] != x] &@ FactorInteger[x][[;; , -1]]; Select[Range[240], fQ]

CROSSREFS

Cf. A025487, A126706, A332785, A369361, A369636.

Sequence in context: A072904 A268284 A367268 * A054279 A186781 A164711

Adjacent sequences: A387916 A387917 A387918 * A387920 A387921 A387922

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Oct 11 2025

STATUS

approved