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Search: id:A069799
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| A069799 |
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The number obtained by reversing the indices in the prime signature of n. |
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+0
3
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 13, 14, 15, 16, 17, 12, 19, 50, 21, 22, 23, 54, 25, 26, 27, 98, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 250, 41, 42, 43, 242, 75, 46, 47, 162, 49, 20, 51, 338, 53, 24, 55, 686, 57, 58, 59, 150, 61, 62, 147, 64, 65
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If n = p^a*q^b*r^c then a(n) = p^c*q^b*r^a. If n = p^a*q^b*r^c*s^d then a(n) = p^d*q^c*r^b*s^a.
Squarefree numbers and their powers remain unchanged in this transformation. If the string of indices form a palindrome then also the numbers remain unchanged in this transformation. Integers which are changed are A059404.
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EXAMPLE
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a(24) = 54 as 24 = 2^3*3 and 54= 2*3^3.
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MATHEMATICA
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f[n_] := Block[{a = Transpose[ FactorInteger[n]], m = n}, If[ Length[a] == 2, Apply[ Times, a[[1]]^Reverse[a[[2]] ]], m]]; Table[ f[n], {n, 1, 65}]
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CROSSREFS
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Cf. A059404.
Sequence in context: A032994 A072356 A105119 this_sequence A085079 A033000 A130573
Adjacent sequences: A069796 A069797 A069798 this_sequence A069800 A069801 A069802
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 13 2002
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com) and Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 15 2002
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