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A275693
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Lexicographically earliest increasing sequence such that the a(n)th term of the sequence has n noncomposite divisors.
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1
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1, 2, 4, 6, 7, 30, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 2330
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OFFSET
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1,2
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COMMENTS
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We let tau_nc(n) = number of noncomposite divisors of n = A083399(n) = A001221(n) + 1 = omega(n) + 1.
Primorial numbers from A002110 are terms.
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LINKS
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FORMULA
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tau_nc(a(a(n))) = A083399(a(a(n))) = A001221(a(a(n))) + 1 = omega(a(a(n))) + 1 = n.
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EXAMPLE
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a(1)=1 because tau_nc(1)=1; a(2)=2 because tau_nc(2)=2; a(3) cannot be 3 because tau_nc(3)=2, a(3)=4 (4 is the smallest number x>3); if a(3)=4, a(4) must be the smallest number x>a(3) with 3 noncomposite divisors, a(4)=6; a(6) must be number with 4 noncomposite divisors and must keep increase of the sequence, a(6)=30; a(5)=7 because 7>a(4); a(7) must be the smallest number with 5 noncomposite divisors because a(5)=7, a(7)=210; if a(6)=30, a(30) must be the smallest number x>a(7) with 6 noncomposite divisors and must keep increase of the sequence, a(30)=2310; a(8)-a(29) are numbers from interval 211-232; etc...
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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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