A325564 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A325563(n) except f(1) = 0.

1, 2, 2, 3, 2, 4, 2, 5, 4, 6, 2, 7, 2, 8, 6, 9, 2, 10, 2, 11, 8, 12, 2, 13, 2, 14, 10, 15, 2, 16, 2, 17, 4, 18, 8, 19, 2, 20, 4, 21, 2, 22, 2, 23, 16, 24, 2, 25, 8, 26, 18, 27, 2, 28, 2, 29, 4, 30, 2, 31, 2, 32, 22, 33, 6, 34, 2, 35, 2, 36, 2, 37, 2, 38, 16, 39, 2, 40, 2, 41, 2, 42, 2, 43, 18, 44, 2, 45, 2, 46, 2, 47, 32, 48, 20, 49, 2, 50, 34, 51, 2, 52, 2, 53, 16

Offset: 1

Author

Antti Karttunen, May 11 2019

Keywords

• nonn

Comments

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j) => A325563(i) = A325563(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A325563.

Programs

PARI

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A325563(n) = if(1==n,n, my(p = Pol(binary(n))*Mod(1, 2)); fordiv(n,d,if((d>1),my(q = Pol(binary(n/d))*Mod(1, 2)); if(0==(p%q), return(n/d)))));
Aux325564(n) = if(1==n,0,A325563(n));
v325564 = rgs_transform(vector(up_to,n,Aux325564(n)));
A325564(n) = v325564[n];