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A324705
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Lexicographically earliest sequence containing 1 and all composite numbers divisible by prime(m) for some m already in the sequence.
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12
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1, 4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32, 34, 35, 36, 38, 39, 40, 42, 44, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 70, 72, 74, 76, 77, 78, 80, 82, 84, 86, 87, 88, 90, 91, 92, 94, 95, 96, 98, 100, 102, 104, 105, 106
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listen;
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OFFSET
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1,2
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COMMENTS
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A self-describing sequence, similar to A304360.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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Table of n, a(n) for n=1..65.
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
4: {1,1}
6: {1,2}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
14: {1,4}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
34: {1,7}
35: {3,4}
36: {1,1,2,2}
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MATHEMATICA
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aQ[n_]:=Switch[n, 1, True, _?PrimeQ, False, _, !And@@Cases[FactorInteger[n], {p_, k_}:>!aQ[PrimePi[p]]]];
Select[Range[200], aQ]
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CROSSREFS
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Complement of A324697.
Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
Cf. A324694, A324695, A324696, A324698, A324699, A324700, A324701, A324702, A324703, A324704.
Sequence in context: A185604 A054023 A330948 * A032583 A175074 A063127
Adjacent sequences: A324702 A324703 A324704 * A324706 A324707 A324708
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Mar 11 2019
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STATUS
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approved
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