A355832 Lexicographically earliest infinite sequence such that a(i) = a(j) => A354347(i) = A354347(j) for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 19 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of A354347, which is the Dirichlet inverse of A345000(n) = gcd(A003415(n), A003415(A276086(n))).

Links

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

Crossrefs

Cf. A003415, A276086, A345000, A354347, A355831.

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); };
A345000(n) = gcd(A003415(n),A003415(A276086(n)));
v354347 = DirInverseCorrect(vector(up_to,n,A345000(n)));
v355832 = rgs_transform(v354347);
A355832(n) = v355832[n];