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A090883
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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)*n + (e3)*(n^2) + (e4)*(n^3) + ... + (ek)*(n^(k-1)) + ...
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7
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0, 1, 3, 2, 25, 7, 343, 3, 18, 101, 14641, 14, 371293, 2745, 240, 4, 24137569, 37, 893871739, 402, 9282, 234257, 78310985281, 27, 1250, 11881377, 81, 21954, 14507145975869, 931, 819628286980801, 5, 1185954, 1544804417, 44100, 74
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Replace "(ek)*(n^(k-1))" with "(ek)*(x^(k-1))" for all k 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, A090881, A090882, A090884.
Sequence in context: A151475 A105525 A165714 * A100645 A132960 A009574
Adjacent sequences: A090880 A090881 A090882 * A090884 A090885 A090886
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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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