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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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2
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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
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) is the smallest number such that Nest[EulerPhi, A002110, a(n)]=1
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EXAMPLE
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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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MATHEMATICA
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Array[-2 + Length@ FixedPointList[EulerPhi, Product[Prime@ i, {i, #}]] &, 58] (* Michael De Vlieger, Nov 20 2017 *)
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PROG
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(PARI) a(n)=my(t=prod(i=1, n, prime(i)-1), s=1); while(t>1, t=eulerphi(t); s++); s \\ Charles R Greathouse IV, Jan 06 2016
(PARI) A003434(n)=my(s); while(n>1, n=eulerphi(n); s++); s
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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