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A361102 1 together with numbers having at least two distinct prime factors. 16
1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This is the union of 1 and A024619. It is the sequence C used in the definition of A360519. Since C is central to the analysis of A360519 it deserves its own entry.
This has the same relationship to A024619 as A000469 does to A120944 for squarefree numbers.
LINKS
FORMULA
From Peter Luschny and Michael De Vlieger, May 17 2023: (Start)
The sequence is the complement of the prime powers in the positive integers, a = A000027 \ A246655.
k is in this sequence <=> k divides lcm(1, 2, ..., k-1). (End)
This sequence is {1} U { A120944 U A126706 } = {1} U A024619. - Michael De Vlieger, May 17 2023
MAPLE
isa := n -> is(irem(ilcm(seq(1..n-1)), n) = 0):
aList := upto -> select(isa, [seq(1..upto)]):
aList(112); # Peter Luschny, May 17 2023
MATHEMATICA
Select[Range[120], Not@*PrimePowerQ] (* Michael De Vlieger, May 17 2023 *)
PROG
(SageMath)
def A361102List(upto: int) -> list[int]:
return sorted(Set(1..upto).difference(prime_powers(upto)))
print(A361102List(112)) # Peter Luschny, May 17 2023
CROSSREFS
Sequence in context: A064040 A168638 A024619 * A335080 A323304 A325411
KEYWORD
nonn
AUTHOR
EXTENSIONS
Offset set to 1 by Peter Luschny, May 17 2023
STATUS
approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)