A096852 a(n) is the length of terminal cycle of the trajectory of f(x)=phi(sigma(x)) if started at 2^n.

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, 12, 12, 1

Offset: 0

Author

Labos Elemer, Jul 16 2004

Keywords

• nonn

Examples

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

Crossrefs

Cf. A095955, A095956, A096849, A096850.

Programs

Mathematica

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}]

PARI

f(x)=eulerphi(sigma(x))
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

Formula

a(n) = A095955(2^n). - Charles R Greathouse IV, Nov 27 2013

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jul 17 2004