A339874 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A052126(n) for n > 1, and f(1) = 0.

1, 2, 2, 3, 2, 3, 2, 4, 5, 3, 2, 4, 2, 3, 5, 6, 2, 7, 2, 4, 5, 3, 2, 6, 8, 3, 9, 4, 2, 7, 2, 10, 5, 3, 8, 11, 2, 3, 5, 6, 2, 7, 2, 4, 9, 3, 2, 10, 12, 13, 5, 4, 2, 14, 8, 6, 5, 3, 2, 11, 2, 3, 9, 15, 8, 7, 2, 4, 5, 13, 2, 16, 2, 3, 17, 4, 12, 7, 2, 10, 18, 3, 2, 11, 8, 3, 5, 6, 2, 14, 12, 4, 5, 3, 8, 15, 2, 19, 9, 20, 2, 7, 2, 6, 17

Offset: 1

Author

Antti Karttunen, Dec 25 2020

Keywords

• nonn

Comments

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j),

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

a(i) = a(j) => A322826(i) = A322826(j).

Links

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

Crossrefs

Cf. A052126, A322826.

Cf. also A305800, A300226, A334107, A334108.

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; };
A052126(n) = if(1==n,n,(n/vecmax(factor(n)[, 1])));
Aux339874(n) = if(1==n,0,A052126(n));
v339874 = rgs_transform(vector(up_to, n, Aux339874(n)));
A339874(n) = v339874[n];

Formula

a(1) = 1; for n > 1, a(n) = 1 + A322826(n).