A335880 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jun 29 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A329697(n), A331410(n)].

For all i, j:

A324400(i) = A324400(j) => a(i) = a(j),

a(i) = a(j) => A334861(i) = A334861(j),

a(i) = a(j) => A335875(i) = A335875(j),

a(i) = a(j) => A335877(i) = A335877(j),

a(i) = a(j) => A335881(i) = A335881(j).

Links

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

Crossrefs

Cf. A329697, A331410, A334861, A335875, A335877, A335881.

Cf. also A324400, A334867.

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; };
A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
Aux335880(n) = [A329697(n),A331410(n)];
v335880 = rgs_transform(vector(up_to, n, Aux335880(n)));
A335880(n) = v335880[n];