A361026 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Mar 03 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A003557(n), A053669(n)].

For all i, j >= 1,

A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),

a(i) = a(j) => A007814(i) = A007814(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A003557, A007814, A053669.

Cf. A305801, A353520.

Programs

PARI

up_to = 100000;
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; };
A003557(n) = (n/factorback(factorint(n)[, 1]));
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
Aux361026(n) = [A003557(n), A053669(n)];
v361026 = rgs_transform(vector(up_to,n,Aux361026(n)));
A361026(n) = v361026[n];