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A090881
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Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then a(n) = e1 + (e2)*4 + (e3)*16 + (e4)*64 + ... + (ek)*(4^(k-1)) + ...
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5
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0, 1, 4, 2, 16, 5, 64, 3, 8, 17, 256, 6, 1024, 65, 20, 4, 4096, 9, 16384, 18, 68, 257, 65536, 7, 32, 1025, 12, 66, 262144, 21, 1048576, 5, 260, 4097, 80, 10, 4194304, 16385, 1028, 19, 16777216, 69, 67108864, 258, 24, 65537, 268435456, 8, 128, 33, 4100, 1026
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Replace "4" with "x" and extend the definition of a to positive rationals and a becomes an isomorphism between positive rationals under multiplication and polynomials over Z under addition. This remark generalizes A001222, A048675 and A054841: evaluate said polynomial at x=1, x=2 and x=10, respectively.
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REFERENCES
| Joseph J. Rotman, The Theory of Groups: An Introduction, 2nd ed. Boston: Allyn and Bacon, Inc. 1973. Page 9, problem 1.26.
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LINKS
| Sam Alexander, Post to sci.math.
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CROSSREFS
| Cf. A001222, A048675, A054841, A090880, A090882, A090883, A090884.
Sequence in context: A130042 A109922 A090640 * A191452 A110485 A154383
Adjacent sequences: A090878 A090879 A090880 * A090882 A090883 A090884
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KEYWORD
| easy,nonn
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AUTHOR
| Sam Alexander (amnalexander(AT)yahoo.com), Dec 12 2003
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 20 2003
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