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A102440
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Replace each prime factor of n that is greater than 3 with the greatest semiprime less than it.
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6
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1, 2, 3, 4, 4, 6, 6, 8, 9, 8, 10, 12, 10, 12, 12, 16, 15, 18, 15, 16, 18, 20, 22, 24, 16, 20, 27, 24, 26, 24, 26, 32, 30, 30, 24, 36, 35, 30, 30, 32, 39, 36, 39, 40, 36, 44, 46, 48, 36, 32, 45, 40, 51, 54, 40, 48, 45, 52, 58, 48, 58, 52, 54, 64, 40, 60, 65, 60, 66, 48, 69, 72, 69
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with prime(i) -> (if i<=2 then prime(i) else A102415(i)).
a(n) <= n and a(n) = n iff n is 3-smooth, see A003586.
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EXAMPLE
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a(99) = a(3*3*11) -> 3*3*[11->2*5] = 3*3*2*5 = 90.
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MATHEMATICA
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g[p_] := (* greatest semiprime less than prime p *) g[p] = For[k = p - 1, True, k--, If[PrimeOmega[k] == 2, Return[k]]];
a[n_] := Product[{p, e} = pe; If[p <= 3, p, g[p]]^e, {pe, FactorInteger[n]}];
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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