A366297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A359589(i) = A359589(j) for all i, j >= 1, where A359589 is Dirichlet inverse of function f(n) = (-1 + gcd(A003415(n), A276086(n))).

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

Offset: 1

Author

Antti Karttunen, Oct 07 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A359589.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A359595(i) = A359595(j).

Links

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

Crossrefs

Cf. A276086, A305800, A327858, A359589, A359595.

Cf. also A366296.

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(dA003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n), A276086(n));
v366297 = rgs_transform(DirInverseCorrect(vector(up_to,n,A327858(n)-1)));
A366297(n) = v366297[n];