A369467 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369465(i) = A369465(j) and A369465(A163511(i)) = A369465(A163511(j)), for all i, j >= 1.

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 5, 2, 6, 2, 7, 1, 8, 4, 9, 3, 10, 5, 11, 2, 12, 6, 13, 2, 5, 7, 2, 1, 14, 8, 15, 4, 16, 9, 17, 3, 18, 10, 19, 5, 20, 11, 21, 2, 22, 12, 23, 6, 24, 13, 25, 2, 26, 5, 27, 7, 11, 2, 28, 1, 29, 14, 30, 8, 31, 15, 32, 4, 33, 16, 34, 9, 35, 17, 36, 3, 37, 18, 38, 10, 39, 19, 40, 5, 41, 20, 42, 11, 43, 21, 44, 2, 45, 22

Offset: 1

Author

Antti Karttunen, Jan 28 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A369458(n), A369465(n)], or equally, of the ordered pair [A369459(n), A369466(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. A000265, A003415, A003602, A163511, A349905, A369458, A369459, A369465, A369466.

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]));
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));
A369465(n) = A003415(A000265(n));
Aux369467(n) = [A369465(n), A369465(A163511(n))];
v369467 = rgs_transform(vector(up_to, n, Aux369467(n)));
A369467(n) = v369467[n];