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A110884
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a(n) = limiting ratio of successive terms in the trajectory of 1 under the map m -> n*phi(m).
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0
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1, 1, 1, 2, 2, 2, 2, 4, 3, 4, 4, 4, 4, 4, 4, 8, 8, 6, 6, 8, 6, 8, 8, 8, 10, 8, 9, 8, 8, 8, 8, 16, 8, 16, 8, 12, 12, 12, 12, 16, 16, 12, 12, 16, 12, 16, 16, 16, 14, 20, 16, 16, 16, 18, 20, 16, 18, 16, 16, 16, 16, 16, 18, 32, 16, 16, 16, 32, 16, 16, 16, 24, 24, 24, 20, 24, 16, 24, 24, 32, 27
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OFFSET
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1,4
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COMMENTS
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Let c(1)=1 and c(k+1)=n*phi(c(k)). Then c(k+1)/c(k) is a decreasing sequence of integers, so eventually becomes constant. a(n) is the ratio between terms once that becomes constant. (In fact, as soon as a ratio repeats, it remains constant from that point on.)
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LINKS
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FORMULA
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If p prime, a(p)=a(p-1). If every prime divisor of m divides n, a(n*m)=a(n)*m.
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EXAMPLE
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For n=25, the sequence m -> n*phi(m) is 1,25,500,5000,50000,...; the ratios are 25,20,10,10,...; so a(25)=10.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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