A096852 - OEIS

%I #7 Nov 27 2013 12:13:25

%S 1,1,2,1,3,2,2,1,2,2,6,2,1,6,2,1,2,3,11,11,2,2,15,15,18,18,18,18,12,

%T 12,12,1

%N a(n) is the length of terminal cycle of the trajectory of f(x)=phi(sigma(x)) if started at 2^n.

%F a(n) = A095955(2^n). - _Charles R Greathouse IV_, Nov 27 2013

%e n=18: start = 262144 and the corresponding 11-cycle is 262144, 524286, [368640, 381024, 326592, 550368, 435456, 580608, 851840, 552960, 524160, 442368, 432000], 368640, ...

%t g[n_] := EulerPhi[ DivisorSigma[1, n]]; f[n_] := Block[{lst = NestWhileList[g, n, UnsameQ, All]}, -Subtract @@ Flatten[ Position[lst, lst[[ -1]]]]]; Table[ f[2^n], {n, 0, 20}]

%o (PARI) f(x)=eulerphi(sigma(x))

%o a(n)=my(t=f(2^n), h=f(t), s); while(t!=h, t=f(t); h=f(f(h))); t=f(t); h=f(t); s=1; while(t!=h, s++; t=f(t); h=f(f(h))); s \\ _Charles R Greathouse IV_, Nov 27 2013

%Y Cf. A095955, A095956, A096849, A096850.

%K nonn

%O 0,3

%A _Labos Elemer_, Jul 16 2004

%E Edited, corrected and extended by _Robert G. Wilson v_, Jul 17 2004