A328765 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A328763(n), except for odd numbers > 1, f(n) = 0.

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

Offset: 0

Author

Antti Karttunen, Oct 28 2019

Keywords

• nonn

Comments

For all i, j:

A319701(i) = A319701(j) => a(i) = a(j),

a(i) = a(j) => A328578(i) = A328578(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A276086, A319701, A328578, A328613, A328763, A328764.

Programs

PARI

up_to = 32768;
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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328613(n) = { my(m=1, p=2); while(n, m *= p^valuation(n,p); n = n\p; p = nextprime(1+p)); (m*p); };
A328763(n) = A328613(A276086(n));
Aux328765(n) = if((n>1)&&(n%2),0,A328763(n));
v328765 = rgs_transform(vector(1+up_to, n, Aux328765(n-1)));
A328765(n) = v328765[1+n];