A366259 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366258(i) = A366258(j) for all i, j >= 1, where A366258 is Dirichlet inverse of gcd(n, A366275(n)).

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

Offset: 1

Author

Antti Karttunen, Oct 07 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A366258.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A366275, A366283, A366258.

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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
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));
A366275(n) = A163511(A057889(n));
A366283(n) = gcd(n,A366275(n));
v366259 = rgs_transform(DirInverseCorrect(vector(up_to,n,A366283(n))));
A366259(n) = v366259[n];