Search: id:A060367
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%I A060367
%S A060367 1,1,2,2,4,3,6,5,6,6,10,6,12,9,9,10,16
%N A060367 Average order of an element in a cyclic group of order n rounded down.
%F A060367 Sequence A057660 gives the sum of the orders of the elements in a cyclic 
               group with n elements so a(n) = [A057660(n) / n] = [Sum_{k=1..n} 
               1/g.c.d.(n, k)] = [Sum of 1/d times phi(n/d)] for all divisors d 
               of n, where phi is Euler's phi function. This sum may also be expressed 
               as the product of (p^(2*e(p)+1)+1)/((p+1) * p^e(p)) over all prime 
               divisors p of n where the canonical factorization of n is the product 
               of p^e(p), the e(p) being the exponents of the power of p in the 
               factorization (as usual [] denotes floor)
%Y A060367 A057660, A018804.
%Y A060367 Sequence in context: A060766 A029578 A054345 this_sequence A062968 A053197 
               A088145
%Y A060367 Adjacent sequences: A060364 A060365 A060366 this_sequence A060368 A060369 
               A060370
%K A060367 nonn
%O A060367 0,3
%A A060367 Avi Peretz (njk(AT)netvision.net.il), Apr 01 2001

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