A369466 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j), for all i, j >= 1.

1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 4, 1, 2, 3, 2, 2, 5, 2, 2, 2, 5, 2, 6, 2, 2, 4, 2, 1, 7, 2, 8, 3, 2, 2, 9, 2, 2, 5, 2, 2, 10, 2, 2, 2, 7, 5, 11, 2, 2, 6, 9, 2, 12, 2, 2, 4, 2, 2, 13, 1, 14, 7, 2, 2, 15, 8, 2, 3, 2, 2, 16, 2, 14, 9, 2, 2, 17, 2, 2, 5, 12, 2, 18, 2, 2, 10, 11, 2, 19, 2, 20, 2, 2, 7, 21, 5, 2, 11

Offset: 1

Author

Antti Karttunen, Jan 27 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of A369465.

For all i, j >= 1: A003602(i) = A003602(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A000265, A003415, A003602, A064989, A349905, A369465.

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; };
A000265(n) = (n>>valuation(n,2));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369465(n) = A003415(A000265(n));
v369466 = rgs_transform(vector(up_to, n, A369465(n)));
A369466(n) = v369466[n];