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

1,1

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

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

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[#]} &]

Crossrefs

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

Sequence in context: A367539 A093373 A096849 * A326980 A281005 A080259

Adjacent sequences: A369358 A369359 A369360 * A369362 A369363 A369364

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 21 2024

Status

approved