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A113645
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Numbers n such that sum of exponents in prime factorization of n (i.e. A001222(n)) is >= each prime divisor of n.
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0
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4, 8, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 80, 81, 96, 108, 120, 128, 144, 160, 162, 180, 192, 200, 216, 240, 243, 256, 270, 288, 300, 320, 324, 360, 384, 400, 405, 432, 448, 450, 480, 486, 500, 512, 540, 576, 600, 640, 648, 672, 675, 720, 729, 750, 768
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| A number n is included if A006530(n) <= A001222(n).
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EXAMPLE
| 12 = 2^2 *3^1. Since the sum of the prime-factorization exponents, 2+1 = 3, is >= the largest prime dividing 12, which is 3, then 12 is included in the sequence.
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MATHEMATICA
| fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Max[First /@ f]]; Select[ Range[2, 800], fQ@ # &] (* Robert G. Wilson v *)
qu[n_]:=n>1&&Block[{f=Transpose@FactorInteger@n, s}, s=Plus@@f[[2]]; s>=Max@f[[1]]]; L ={}; Do[If[qu[n], Print[n]; AppendTo[L, n]], {n, 1000}]; L (Resta)
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CROSSREFS
| Cf. A001222, A006530; a proper subset of A068936.
Sequence in context: A130702 A053806 A068306 * A190714 A086133 A100716
Adjacent sequences: A113642 A113643 A113644 * A113646 A113647 A113648
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Jan 15 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 16 2006
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