

A090884


There exists an isomorphism from the positive rationals under multiplication to Z[x] under addition, defined by f(q) = e1 + (e2)x + (e3)(x^2) +...+ (ek)(x^(k1)) + ... (where e_i is the exponent of the ith prime in q's prime factorization) The a(n) above are calculated by a(n) = f^(1)[d/dx f(n)] (In other words: differentiate n's image in Z[x] and return to Q).


6



1, 1, 2, 1, 9, 2, 125, 1, 4, 9, 2401, 2, 161051, 125, 18, 1, 4826809, 4, 410338673, 9, 250, 2401, 16983563041, 2, 81, 161051, 8, 125, 1801152661463, 18, 420707233300201, 1, 4802, 4826809, 1125, 4, 25408476896404831, 410338673, 322102, 9
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OFFSET

1,3


REFERENCES

Joseph J. Rotman, The Theory of Groups: An Introduction, 2nd ed. Boston: Allyn and Bacon, Inc. 1973. Page 9, problem 1.26.


LINKS

Table of n, a(n) for n=1..40.
Sam Alexander, Post to sci.math.


CROSSREFS

Cf. A001222, A048675, A054841, A090880, A090881, A090882, A090883.
Sequence in context: A243999 A223141 A021460 * A095888 A160510 A124776
Adjacent sequences: A090881 A090882 A090883 * A090885 A090886 A090887


KEYWORD

easy,nonn


AUTHOR

Sam Alexander, Dec 12 2003


EXTENSIONS

More terms from Ray Chandler, Dec 20 2003


STATUS

approved



