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A067599
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Decimal encoding of the prime factorization of n: concatenation of prime factors and exponents.
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16
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21, 31, 22, 51, 2131, 71, 23, 32, 2151, 111, 2231, 131, 2171, 3151, 24, 171, 2132, 191, 2251, 3171, 21111, 231, 2331, 52, 21131, 33, 2271, 291, 213151, 311, 25, 31111, 21171, 5171, 2232, 371, 21191, 31131, 2351, 411, 213171, 431, 22111, 3251, 21231
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OFFSET
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2,1
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COMMENTS
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If n has prime factorization p_1^e_1 * ... * p_r^e_r with p_1 < ... < p_r, then its decimal encoding is p_1 e_1...p_r e_r. For example, 15 = 3^1 * 5^1, so has decimal encoding 3151.
Sequence A068633 is a duplicate, up to a conventional initial term a(1)=11.
The earliest duplicate is a(223) = 2231 = a(12). There is no fixed point below 3*10^6. - M. F. Hasler, Oct 06 2013
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LINKS
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EXAMPLE
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The prime factorization of 24 = 2^3 * 3^1 has corresponding encoding 2331. So a(24) = 2331.
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MAPLE
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with(ListTools): with(MmaTranslator[Mma]): seq(FromDigits(FlattenOnce(ifactors(n)[2])), n=2..46); # Wolfdieter Lang, Aug 16 2014
# second Maple program:
a:= n-> parse(cat(map(i-> i[], sort(ifactors(n)[2]))[])):
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MATHEMATICA
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f[n_] := FromDigits[ Flatten[ IntegerDigits[ FactorInteger[ n]]]]; Table[ f[n], {n, 2, 50} ]
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PROG
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(PARI) A067599(n)=eval(concat(concat([""], concat(Vec(factor(n)~))~))) \\ - M. F. Hasler, Oct 06 2013
(Haskell)
import Data.Function (on)
a067599 n = read $ foldl1 (++) $
zipWith ((++) `on` show) (a027748_row n) (a124010_row n) :: Integer
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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