%I A090880
%S A090880 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,
%T A090880 244,9,29,19683,13,59049,5,84,730,36,8,177147,2188,246,12,531441,31,
%U A090880 1594323,83,15,6562,4782969,7,54,19,732,245,14348907,10,90,30,2190
%N A090880 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)) + ...
%C A090880 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.
%D A090880 Joseph J. Rotman, The Theory of Groups: An Introduction, 2nd ed. Boston: 
               Allyn and Bacon, Inc. 1973. Page 9, problem 1.26.
%H A090880 Sam Alexander, <a href="http://tinyurl.com/yzea">Post to sci.math</a>
               .
%Y A090880 Cf. A001222, A048675, A054841, A090881, A090882, A090883, A090884.
%Y A090880 Sequence in context: A104005 A134562 A090639 this_sequence A064614 A016650 
               A033313
%Y A090880 Adjacent sequences: A090877 A090878 A090879 this_sequence A090881 A090882 
               A090883
%K A090880 easy,nonn
%O A090880 1,3
%A A090880 Sam Alexander (amnalexander(AT)yahoo.com), Dec 12 2003
%E A090880 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 20 
               2003