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Let f(n) = A003434(n) be the number of iterations of phi needed to reach 1. Then a(n) = max(f(1), f(2), ..., f(n)).
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%I #5 Apr 11 2022 18:14:56

%S 0,1,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

%T 5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7

%N Let f(n) = A003434(n) be the number of iterations of phi needed to reach 1. Then a(n) = max(f(1), f(2), ..., f(n)).

%o (PARI) epr(m,c)=if (c>0,m=eulerphi(m); c--; epr(m,c),m) x=1; for (n=1,100, while (epr(n,x)>1, x++); print1(x","))

%Y Cf. A003434.

%K easy,nonn

%O 1,3

%A _Jon Perry_, Jan 09 2003

%E Description corrected by Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003