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A369361
Numbers that are not products of primorials.
3
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
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[#]} &]
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jan 21 2024
STATUS
approved