A053036 Number of values which are not powers of 2 in the trajectory when A051953 (cototient function) is repeatedly applied starting with n!.

1, 1, 2, 2, 4, 5, 7, 7, 9, 20, 22, 23, 35, 38, 35, 35, 48, 54, 62, 79, 79, 85, 64, 65, 108, 124, 133, 130, 120, 158, 128, 128, 170, 181, 179, 189, 220, 181, 226, 228, 192, 255, 268, 268, 269, 292, 291, 286, 317, 324, 337, 288, 354, 352, 384, 378, 396, 345, 426, 393

Offset

1,3

Comments

Unlike the analogous sequence based on A000005, the non-powers 2 which emerge during iteration are initial, consecutive iterates, except the last one=0.

Links

Table of n, a(n) for n=1..60.

Example

n=9, initial value=9!=362880, the successive iterates when the cototient function (A051953) is repeatedly applied are: {362880, 279936, 186624, 124416, 82944, 55296, 36864, 24576, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0}. This includes 8 initial and 1 terminal (it is the 0) which are not powers of 2. So a(9)=8+1=9. Beside 15 2-powers appear.

Prog

(PARI) cototient(x)= x - eulerphi(x)
FunctionIterate(f, x, t)= {local(retval); retval = vector(0); while(x!=t, x = eval(concat(f, "(x)")); retval = concat(retval, x)); retval; }
A053036(x) = {local(li, fa, count); count = 0; li = concat([x! ], FunctionIterate("cototient", x!, 0)); for(i=1, #li, fa = factor(li[i]); if(((matsize(fa)[1] == 1) && (fa[1, 1] == 2)) || (matsize(fa)[1] == 0), 0, count++)); count}
for(i=1, 64, print1(A053036(i), ", ")) \\ Olaf Voß, Feb 20 2008

Crossrefs

Cf. A051953, A053475.

Sequence in context: A325554 A367962 A107849 * A308840 A067957 A120326

Adjacent sequences: A053033 A053034 A053035 * A053037 A053038 A053039

Keyword

nonn

Author

Labos Elemer, Feb 24 2000

Extensions

More terms from Olaf Voß, Feb 20 2008

Status

approved