A369361 Numbers that are not products of primorials.

3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset: 1

Author

Michael De Vlieger, Jan 21 2024

Keywords

• nonn
• easy

Comments

Differs from A080259 in that this sequence includes 18.

Differs from A093373 in that this sequence does not include 30.

Primorials P(n) = A002110(n) are not in this sequence.

Does not contain powers of 2.

Contains odd numbers k > 1.

Numbers that are not the first with their prime signature, complement of A025487. - Peter Munn, Jan 24 2024

Links

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

Crossrefs

Cf. A000079, A002110, A005408, A025487, A046523, A056808, A080259, A093373.

Programs

Mathematica

Select[Range[210], Nor[# == 1, IntegerQ@ Log2[#], And[EvenQ[#1], Union@ Differences@ PrimePi[#2[[All, 1]]] == {1}, AllTrue[Differences@ #2[[All, -1]], # <= 0 &]]] & @@ {#, FactorInteger[#]} &]

Formula

{a(n)} = A000027 \ A025487.

Union of A080259 and A056808, superset of both.

Superset of A005408 \ {1}.

{a(n)} = {k : A046523(k) < k}. - Peter Munn, Jan 24 2024