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A046759
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Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n)<l(n).
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9
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125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875, 2048, 2187, 2197, 2209, 2401, 2560, 2809, 3125, 3481, 3584, 3645, 3721, 4096, 4374, 4375, 4489, 4802, 4913
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OFFSET
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1,1
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COMMENTS
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A050252(a(n)) < A055642(a(n)). [Reinhard Zumkeller, Jun 21 2011]
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Glossary, economical number
J.-M. De Koninck and F. Luca, On strings of consecutive economical numbers of arbitrary length
J.-P. Delahaye, Les chasseurs de nombres premiers
R. G. E. Pinch, Economical numbers.
R. G. E. Pinch, Economical numbers
W. Schneider, Economical Numbers
G. Villemin's Almanach of Numbers, Nombres Economes
Eric Weisstein's World of Mathematics, Economical Number.
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EXAMPLE
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For n=125=5^3, l(n)=3 but D(n)=2.
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MATHEMATICA
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ecoQ[n_] := Total[ Length /@ IntegerDigits /@ Flatten[ FactorInteger[n] /. {p_, 1} -> p]] < Length[ IntegerDigits[n]]; Select[ Range[5000], ecoQ] (* From Jean-François Alcover, Jul 28 2011 *)
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PROG
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(Haskell)
a046759 n = a046759_list !! (n-1)
a046759_list = filter (\n -> a050252 n < a055642 n) [1..]
-- Reinhard Zumkeller, Jun 21 2011
(PARI) is(n)=my(f=factor(n)); sum(i=1, #f[, 1], #Str(f[i, 1])+if(f[i, 2]>1, #Str(f[i, 2])))<#Str(n) && n>1 \\ Charles R Greathouse IV, Feb 01 2013
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CROSSREFS
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Cf. A046758, A046760.
Sequence in context: A195420 A080538 A104233 * A115938 A126895 A202240
Adjacent sequences: A046756 A046757 A046758 * A046760 A046761 A046762
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KEYWORD
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nonn,nice,base,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Eric W. Weisstein
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STATUS
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approved
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