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A324694
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Lexicographically earliest sequence of positive integers divisible by prime(m) for some m not already in the sequence.
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39
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2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 28, 30, 31, 32, 34, 35, 36, 38, 40, 41, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 58, 60, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 80, 82, 84, 85, 86, 88, 90, 92, 93, 94, 95
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OFFSET
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1,1
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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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EXAMPLE
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The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
5: {3}
6: {1,2}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
17: {7}
18: {1,2,2}
20: {1,1,3}
22: {1,5}
23: {9}
24: {1,1,1,2}
25: {3,3}
26: {1,6}
28: {1,1,4}
30: {1,2,3}
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MATHEMATICA
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aQ[n_]:=!And@@Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>aQ[PrimePi[p]]];
Select[Range[100], aQ]
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CROSSREFS
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Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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