A366888 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366887(i) = A366887(j) for all i, j >= 0.

1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 4, 3, 5, 1, 2, 2, 3, 2, 4, 3, 5, 2, 4, 4, 6, 3, 7, 5, 8, 1, 2, 2, 3, 2, 4, 3, 5, 2, 4, 4, 6, 3, 7, 5, 8, 2, 4, 4, 6, 4, 9, 6, 10, 3, 7, 7, 11, 5, 6, 8, 12, 1, 2, 2, 3, 2, 4, 3, 5, 2, 4, 4, 6, 3, 7, 5, 8, 2, 4, 4, 6, 4, 9, 6, 10, 3, 7, 7, 11, 5, 6, 8, 12, 2, 4, 4, 6, 4, 9, 6, 10, 4, 9

Offset: 0

Author

Antti Karttunen, Nov 04 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A366887.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A163511, A206787, A366887.

Cf. also A366881.

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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
A366887(n) = A206787(A163511(n));
v366888 = rgs_transform(vector(1+up_to,n,A366887(n-1)));
A366888(n) = v366888[1+n];