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Search: id:A110884
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| A110884 |
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Limit ratio of m -> n*phi(m). |
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+0
1
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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
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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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 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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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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Cf. Phi A000010.
Sequence in context: A098983 A097576 A029250 this_sequence A155904 A125913 A122386
Adjacent sequences: A110881 A110882 A110883 this_sequence A110885 A110886 A110887
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Sep 19 2005
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