A326202 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 2 and gcd(n,sigma(n)) = 1, with f(n) = n for all other numbers.

1, 2, 3, 3, 3, 4, 3, 3, 3, 5, 3, 6, 3, 7, 8, 3, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 3, 14, 3, 15, 3, 3, 16, 17, 3, 3, 3, 18, 3, 19, 3, 20, 3, 21, 22, 23, 3, 24, 3, 3, 25, 26, 3, 27, 3, 28, 3, 29, 3, 30, 3, 31, 3, 3, 3, 32, 3, 33, 34, 35, 3, 36, 3, 37, 3, 38, 3, 39, 3, 40, 3, 41, 3, 42, 3, 43, 44, 45, 3, 46, 47, 48, 3, 49, 50, 51, 3, 3, 52, 3, 3, 53, 3, 54, 55

Offset: 1

Author

Antti Karttunen, Jul 11 2019

Keywords

• nonn

Comments

For all i, j:

A305801(i) = A305801(j) => A324401(i) = A324401(j) => a(i) = a(j),

a(i) = a(j) => A009194(i) = A009194(j) => A325964(i) = A325964(j).

Links

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

Crossrefs

Cf. A000203, A009194, A014567, A305801, A324401, A325964.

Cf. also A326200, A326201, A326203.

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; };
Aux326202(n) = if((n>2) && (1==gcd(n,sigma(n))),0,n);
v326202 = rgs_transform(vector(up_to, n, Aux326202(n)));
A326202(n) = v326202[n];