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A324705
Lexicographically earliest sequence containing 1 and all composite numbers divisible by prime(m) for some m already in the sequence.
12
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
OFFSET
1,2
COMMENTS
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.
EXAMPLE
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}
MATHEMATICA
aQ[n_]:=Switch[n, 1, True, _?PrimeQ, False, _, !And@@Cases[FactorInteger[n], {p_, k_}:>!aQ[PrimePi[p]]]];
Select[Range[200], aQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 11 2019
STATUS
approved