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Search: id:A060367
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| A060367 |
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Average order of an element in a cyclic group of order n rounded down. |
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+0
1
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| 1, 1, 2, 2, 4, 3, 6, 5, 6, 6, 10, 6, 12, 9, 9, 10, 16
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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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)
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CROSSREFS
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A057660, A018804.
Sequence in context: A060766 A029578 A054345 this_sequence A062968 A053197 A088145
Adjacent sequences: A060364 A060365 A060366 this_sequence A060368 A060369 A060370
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KEYWORD
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nonn
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AUTHOR
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Avi Peretz (njk(AT)netvision.net.il), Apr 01 2001
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