Search: id:A102190
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%I A102190
%S A102190 1,1,1,1,2,1,1,2,1,4,1,1,2,2,1,6,1,1,2,4,1,2,6,1,1,4,4,1,10,1,1,2,2,2,
               4,
%T A102190 1,12,1,1,6,6,1,2,4,8,1,1,2,4,8,1,16,1,1,2,2,6,6,1,18,1,1,2,4,4,8,1,2,
               6,
%U A102190 12,1,1,10,10,1,22,1,1,2,2,2,4,4,8,1,4,20,1,1,12,12,1,2,6,18,1,1,2,6,6
%N A102190 Triangle read by rows: coefficients of cycle index polynomial for the 
               cyclic group C_n, Z(C_n,x), multiplied by n.
%C A102190 Row n gives the coefficients of x[k]^{n/k} with increasing divisors k 
               of n.
%C A102190 The length of row n is tau(n) = A000005(n) (number of divisors of n, 
               including 1 and n).
%D A102190 F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1994; pp. 181 and 
               184.
%H A102190 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A102190.text">
               More terms and comments.</a>
%H A102190 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CycleIndex.htmlt">Cycle Index.</a>
%F A102190 a(n, m)= phi(k(m)), m=1..tau(n), n>=1, with k(m) the m-th divisor of 
               n, written in increasing order.
%F A102190 Z(C_n, x):=sum(sum(phi(k)*x[k]^{n/k}, k|n))/n, where phi(n)= A000010(n) 
               (Euler's totient function) and k|n means 'k divides n'. Cf. Harary 
               reference and MathWorld link.
%e A102190 [1], [1, 1], [1, 2], [1, 1, 2], [1, 4], [1, 1, 2, 2], [1, 6],...
%e A102190 Z(C_6,x)=(1*x[1]^6 + 1*x[2]^3 + 2*x[3]^2 + 2*x[6]^1)/6.
%e A102190 a(6,1)=phi(1)=1, a(6,2)=phi(2)=1, a(6,3)=phi(3)=2, a(6,4)=phi(6)=2.
%Y A102190 Sequence in context: A033809 A046067 A132066 this_sequence A138650 A137843 
               A130194
%Y A102190 Adjacent sequences: A102187 A102188 A102189 this_sequence A102191 A102192 
               A102193
%K A102190 nonn,easy,tabf
%O A102190 1,5
%A A102190 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Feb 15 2005

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