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A053096
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When the Euler phi function is iterated with initial value A002110(n)=primorial, a(n)=number of iterations required to reach the fixed number=1.
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1
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1, 2, 4, 6, 9, 12, 16, 19, 23, 27, 31, 35, 40, 44, 49, 54, 59, 64, 69, 74, 79, 84, 90, 96, 102, 108, 114, 120, 125, 131, 136, 142, 149, 155, 161, 167, 173, 178, 185, 191, 198, 204, 210, 217, 223, 229, 235, 241, 248, 254, 261, 268, 275, 282, 290, 297, 304, 310
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OFFSET
| 1,2
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COMMENTS
| Analogous to A053025, A053034, A053044. For comparison: iteration of e.g. A000005 to primorial i.v. is trivially computable: q(n)=A002110(n),d[q(n)]=2^n, d[d[q(n)]]=n+1 and so A036450[A002110(n)]=A000005(n+1).
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FORMULA
| a(n) is the smallest number such that Nest[EulerPhi, A002110, a(n)]=1
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EXAMPLE
| n=7, A002110(7)=510510; the corresponding iteration chain is: {510510,92160,24576,8192,4096,2048,1024,512,256,128,64,32,16,8,4,2,1}.Its length is 17, so the required number of iterations is a(7)=16.
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CROSSREFS
| A000010, A002110.
Sequence in context: A180107 A134678 A135146 * A155752 A145801 A033291
Adjacent sequences: A053093 A053094 A053095 * A053097 A053098 A053099
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Feb 28 2000
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