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Search: id:A090882
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| A090882 |
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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)*5 + (e3)*25 + (e4)*125 + ... + (ek)*(5^(k-1)) + ... |
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6
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| 0, 1, 5, 2, 25, 6, 125, 3, 10, 26, 625, 7, 3125, 126, 30, 4, 15625, 11, 78125, 27, 130, 626, 390625, 8, 50, 3126, 15, 127, 1953125, 31, 9765625, 5, 630, 15626, 150, 12, 48828125, 78126, 3130, 28, 244140625, 131, 1220703125, 627, 35, 390626, 6103515625, 9, 250
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Replace "5" 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, A090880, A090881, A090883, A090884.
Sequence in context: A096035 A036165 A034079 this_sequence A104064 A038244 A135138
Adjacent sequences: A090879 A090880 A090881 this_sequence A090883 A090884 A090885
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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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