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A095955
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Function f(x)=phi(sigma(x)) is iterated with initial value=n; a(n) is the length of cycle into which the trajectory merges.
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20
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1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 3, 2, 3, 1, 1, 3, 1, 1, 3, 3, 1, 3, 3, 1, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 1, 2, 1, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Diagnosis of true cycle of length m: a[j-m]=a[j], but a[j-d]=a[j] cases are excluded for d dividing m.
Length 5 is rare. Example: a[6634509269055173050761216000]=5 and the 5-cycle is {6634509269055173050761216000, 7521613519844726223667200000, 7946886558074859593662464000, 7794495412499746337587200000, 7970172471593905204651622400, 6634509269055173050761216000}. The initial values 2^79=604462909807314587353088 and 2^83= 9671406556917033397649408 after more than 250 transient terms reach this cycle.
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EXAMPLE
| Occurrences of cycle lengths if n<=1000: {C1=110, C2=781, C3=36, C4=67, C5=0, C6=6, C7=0...}.
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MATHEMATICA
| g[n_] := EulerPhi[ DivisorSigma[1, n]]; f[n_] := f[n] = Block[{lst = NestWhileList[g, n, UnsameQ, All ]}, -Subtract @@ Flatten[ Position[lst, lst[[ -1]]]]]; Table[ f[n], {n, 105}] (from Robert G. Wilson v Jul 14 2004)
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CROSSREFS
| Cf. A000010, A000203, A095952, A096887, A095953, A096526, A095954, A096888, A096889, A096890, A095956.
Sequence in context: A054350 A026606 A161175 * A078573 A143786 A035176
Adjacent sequences: A095952 A095953 A095954 * A095956 A095957 A095958
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 13 2004
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