A326193 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = gcd(n,sigma(n)) * (-1)^[gcd(n,sigma(n))==n].

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

Offset: 1

Author

Antti Karttunen, Aug 24 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f, defined as f(n) = -A009194(n) = -n when n is one of multiply-perfect numbers (A007691), otherwise f(n) = A009194(n) = gcd(n,sigma(n)).

For all i, j:

a(i) = a(j) => A326194(i) = A326194(j).

Links

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

Crossrefs

Cf. A000203, A007691, A009194, A326192, A326194.

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; };
Aux326193(n) = { my(u=gcd(n,sigma(n))); u*((-1)^(u==n)); };
v326193 = rgs_transform(vector(up_to, n, Aux326193(n)));
A326193(n) = v326193[n];