A351080 Lexicographically earliest infinite sequence such that a(i) = a(j) => A324198(i) = A324198(j) and A351083(i) = A351083(j) for all i, j >= 0.

1, 2, 2, 3, 4, 2, 2, 5, 6, 3, 7, 2, 4, 2, 2, 8, 9, 2, 10, 2, 11, 3, 2, 2, 12, 13, 2, 3, 4, 2, 2, 2, 4, 3, 14, 15, 16, 2, 2, 17, 18, 2, 19, 2, 12, 8, 2, 2, 4, 19, 13, 3, 12, 2, 10, 20, 21, 3, 2, 2, 4, 2, 2, 22, 12, 2, 2, 2, 4, 3, 23, 2, 24, 2, 2, 25, 4, 26, 2, 2, 27, 3, 2, 2, 28, 20, 2, 3, 6, 2, 10, 29, 12, 3, 2, 2, 4

Offset: 0

Author

Antti Karttunen, Feb 03 2022

Keywords

• nonn
• easy
• look

Comments

Restricted growth sequence transform of the ordered pair [A324198(n), A351083(n)].

For all i, j: a(i) = a(j) => A351084(i) = A351084(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A324198, A351083, A351084.

Cf. also A351085.

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; };
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
A351083(n) = gcd(n, A327860(n));
Aux351080(n) = [A324198(n), A351083(n)];
v351080 = rgs_transform(vector(1+up_to,n,Aux351080(n-1)));
A351080(n) = v351080[1+n];