A053034 Length of sequence when A051953 (cototient function) is repeatedly applied starting with n!.
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
Offset: 1
Keywords
Examples
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.
Programs
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Mathematica
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 *)
Formula
a(n)-1 is the smallest number such that Nest[cototient, n!, a(n)]=0, the fixed point.
Extensions
More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006
Comments