A322826 Lexicographically earliest such sequence a that a(i) = a(j) => A052126(i) = A052126(j) for all i, j.

1, 1, 1, 2, 1, 2, 1, 3, 4, 2, 1, 3, 1, 2, 4, 5, 1, 6, 1, 3, 4, 2, 1, 5, 7, 2, 8, 3, 1, 6, 1, 9, 4, 2, 7, 10, 1, 2, 4, 5, 1, 6, 1, 3, 8, 2, 1, 9, 11, 12, 4, 3, 1, 13, 7, 5, 4, 2, 1, 10, 1, 2, 8, 14, 7, 6, 1, 3, 4, 12, 1, 15, 1, 2, 16, 3, 11, 6, 1, 9, 17, 2, 1, 10, 7, 2, 4, 5, 1, 13, 11, 3, 4, 2, 7, 14, 1, 18, 8, 19, 1, 6, 1, 5, 16

Offset: 1

Author

Antti Karttunen, Dec 27 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A052126, or equally, of A322820.

For all i, j:

A300226(i) = A300226(j) => a(i) = a(j),

a(i) = a(j) => A322813(i) = A322813(j),

a(i) = a(j) => A322819(i) = A322819(j).

For all i, j > 1:

a(i) = a(j) => A001222(i) = A001222(j).

Links

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

Crossrefs

Cf. A001222, A006530, A052126, A305800, A300226, A319994, A319996, A322813, A322819, A322820.

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; };
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A052126(n) = (n/A006530(n));
v322826 = rgs_transform(vector(up_to,n,A052126(n)));
A322826(n) = v322826[n];