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A324854
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Lexicographically earliest sequence containing 1 and all positive integers > 2 whose prime indices already belong to the sequence.
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4
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1, 4, 7, 8, 14, 16, 17, 19, 28, 32, 34, 38, 43, 49, 53, 56, 59, 64, 67, 68, 76, 86, 98, 106, 107, 112, 118, 119, 128, 131, 133, 134, 136, 139, 152, 163, 172, 191, 196, 212, 214, 224, 227, 236, 238, 241, 256, 262, 263, 266, 268, 272, 277, 278, 289, 301, 304
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OFFSET
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1,2
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COMMENTS
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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.
A multiplicative semigroup: if x and y are in the sequence then so is x*y. - Robert Israel, Mar 19 2019
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
4: {1,1}
7: {4}
8: {1,1,1}
14: {1,4}
16: {1,1,1,1}
17: {7}
19: {8}
28: {1,1,4}
32: {1,1,1,1,1}
34: {1,7}
38: {1,8}
43: {14}
49: {4,4}
53: {16}
56: {1,1,1,4}
59: {17}
64: {1,1,1,1,1,1}
67: {19}
68: {1,1,7}
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MAPLE
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S:= {1}:
for n from 3 to 400 do
if map(numtheory:-pi, numtheory:-factorset(n)) subset S then
S:= S union {n}
fi
od:
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MATHEMATICA
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aQ[n_]:=Switch[n, 1, True, 2, False, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]]]];
Select[Range[100], aQ]
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CROSSREFS
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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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