A366791 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366388(j) = A366388(j) and A366788(i) = A366788(j), for all i, j >= 1.

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 5, 4, 7, 1, 8, 5, 9, 3, 10, 6, 11, 2, 12, 5, 13, 4, 11, 7, 14, 1, 15, 8, 16, 5, 17, 9, 13, 3, 18, 10, 8, 6, 14, 11, 19, 2, 10, 12, 20, 5, 21, 13, 22, 4, 5, 11, 20, 7, 6, 14, 11, 1, 19, 15, 23, 8, 24, 16, 6, 5, 16, 17, 25, 9, 12, 13, 24, 3, 26, 18, 19, 10, 15, 8, 26, 6, 8, 14, 16, 11, 27, 19, 6

Offset: 1

Author

Antti Karttunen, Oct 23 2023

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A366388(n), A366788(n)].

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. A003602, A366388, A366788.

Cf. also A334867, A365386, A365388 (compare the scatter plots).

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));
A366388(n) = if(n<=2, 0, if(isprime(n), 1+A366388(primepi(n)), my(f=factor(n)); (apply(A366388, f[, 1])~ * f[, 2])));
Aux366791(n) = [A366388(n), A366388(A163511(n))];
v366791 = rgs_transform(vector(up_to, n, Aux366791(n)));
A366791(n) = v366791[n];