A096994 Number of transient terms if f(x)=phi(sigma(x))=A062401 is iterated at initial value 2^n. Equilibrium terms are listed in A096852.

0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 4, 1, 2, 5, 14, 0, 5, 7, 2, 14, 8, 3, 64, 43, 81, 82, 76, 74, 47, 25, 42, 0

Offset

0,6

Comments

For transient lengths for iterations of A062401(x) or A062402(x) if started at 2^n, A096994(n) + 1 = A096995(n). Corresponding cycle lengths satisfy A096852(n-1) = A096857(n). Behind these observations several relationships stand, e.g., sigma(A062401(x)) = A062402(sigma(x)) or phi(A062402(x)) = A062401(phi(x)).

Links

Table of n, a(n) for n=0..31.

Example

n=0: trajectory = {1,1,..} so a(0)=0;
n=14: transient-length=14, cycle-length=2, a(14)=14, A096852(14)=2; trajectory ={16384, 27000, 23040, 21600, 17280, 15360, 15488, 13824, 9600, 7680, 7200, 12960, 11880, 11520, [10368,14080], 10368, ...}.
Values of a(n) for n > 31, with -1 signifying transient lengths yet unknown after 10^4 iterations of f(x): -1, 7, 51, 70, 23, 39, 11, -1, 37, 107, 30, -1, 145, 25, 21, 36, -1, -1, -1, -1, 31, -1, 452, -1, 449, 447, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 40, -1, -1, -1, -1, -1, -1, -1, 279, -1. - Michael De Vlieger, May 15 2017

Mathematica

With[{nn = 10^3}, Table[Count[Values@ PositionIndex@ #, k_ /; Length@ k == 1] &@ NestList[EulerPhi@ DivisorSigma[1, #] &, 2^n, nn] /. k_ /; k == nn + 1 -> -1, {n, 31}] ] (* Michael De Vlieger, May 15 2017, Version 10 *)

Crossrefs

Cf. A096852, A062401.

Sequence in context: A240181 A079070 A354787 * A035370 A306706 A163000

Adjacent sequences: A096991 A096992 A096993 * A096995 A096996 A096997

Keyword

nonn,more

Author

Labos Elemer, Jul 22 2004

Status

approved