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

Author

Labos Elemer, Feb 24 2000

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A051953, A053475.

Programs

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

Extensions

More terms from Olaf Voß, Feb 20 2008