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Search: id:A053034
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| A053034 |
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Length of sequence when A051953 (cototient function) is repeatedly applied starting with n!. |
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3
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| 2, 3, 5, 7, 10, 13, 17, 20, 24, 32, 36, 40, 50, 55, 59, 63, 72, 78, 87, 101, 103, 114, 107, 112, 135, 151, 160, 167, 164, 188, 179, 184, 208, 219, 220, 230, 260, 241, 266, 273, 261, 298, 311, 313, 321, 338, 342, 340, 367, 377, 389, 374, 410, 410, 438, 436, 457
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The iteration is much slower than the analogue for the divisor function; this sequence is not monotonic, cf. A053475.
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FORMULA
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a(n)-1 is the smallest number so that Nest[cototient, n!, a(n)]=0, the fixed point.
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EXAMPLE
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n=8: initial value=8!=40320, the successive iterates when cototient is iterated are {40320, 31104, 20736, 13824, 9216, 6144, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0}. Observe the parameters: length=20, cototient was applied 19 times, number of initial non-powers of 2 is 6 and 0 is the 7th, while 13 terminal powers of 2 did arise: 4096, ..., 2, 1.
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MATHEMATICA
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a[n_] := Module[{c = 1, x = n!}, While[x != 0, x = x - EulerPhi[x]; c++; ]; c]; - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006
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CROSSREFS
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Cf. A051953, A053475.
Sequence in context: A024180 A008738 A022790 this_sequence A029707 A090499 A022335
Adjacent sequences: A053031 A053032 A053033 this_sequence A053035 A053036 A053037
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 24 2000
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EXTENSIONS
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More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006
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