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A060607
Number of iterations of phi(x) at prime(n) needed to reach 1.
2
1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 8, 7, 7, 7, 7, 6, 8, 7, 8, 7, 7, 8, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 9, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 8, 8, 7, 8, 9, 8, 9, 9, 8, 8, 8, 8, 8, 9, 9, 8, 9, 8, 9, 9, 7, 8, 9, 9, 8, 9, 8, 8, 8, 9, 9, 9, 8
OFFSET
1,2
COMMENTS
Indices of records in this sequence: 1, 2, 3, 5, 7, 13, 23, 33, 55, 116, 184, 384, 719, 1323, 2010, 4289, 6543, 13044, 25685, 45859, 92479, 175261, 298106, 636606, ... The records appear to be A000027. - Michael De Vlieger, Mar 27 2019.
LINKS
FORMULA
a(n) = A003434(A000040(n)). [corrected by Michel Marcus, Mar 27 2019]
MATHEMATICA
Array[-1 + Length@ NestWhileList[EulerPhi, Prime@ #, # > 1 &] &, 105] (* Michael De Vlieger, Mar 27 2019 *)
PROG
(PARI) a(n) = my(t=0, p=prime(n)); while(p>1, t++; p=eulerphi(p)); t; \\ Michel Marcus, Mar 27 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Labos Elemer, Apr 13 2001
EXTENSIONS
Name edited by Michel Marcus, Mar 27 2019
STATUS
approved