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Search: id:A090880
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| A090880 |
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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)*3 + (e3)*9 + (e4)*27 + ... + (ek)*(3^(k-1)) + ... |
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+0
6
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| 0, 1, 3, 2, 9, 4, 27, 3, 6, 10, 81, 5, 243, 28, 12, 4, 729, 7, 2187, 11, 30, 82, 6561, 6, 18, 244, 9, 29, 19683, 13, 59049, 5, 84, 730, 36, 8, 177147, 2188, 246, 12, 531441, 31, 1594323, 83, 15, 6562, 4782969, 7, 54, 19, 732, 245, 14348907, 10, 90, 30, 2190
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Replace "3" 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
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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
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Sam Alexander, Post to sci.math.
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CROSSREFS
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Cf. A001222, A048675, A054841, A090881, A090882, A090883, A090884.
Sequence in context: A104005 A134562 A090639 this_sequence A064614 A016650 A033313
Adjacent sequences: A090877 A090878 A090879 this_sequence A090881 A090882 A090883
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KEYWORD
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easy,nonn
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AUTHOR
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Sam Alexander (amnalexander(AT)yahoo.com), Dec 12 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 20 2003
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