A326192 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A009195(i) = A009195(j) and f(i) = f(j), where f(n) = gcd(n,sigma(n)) * (-1)^[gcd(n,sigma(n))==n] and A009195(n) = gcd(n, phi(n)).

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 7, 9, 10, 2, 11, 2, 12, 6, 7, 2, 13, 14, 7, 15, 16, 2, 17, 2, 18, 9, 7, 2, 19, 2, 7, 6, 20, 2, 21, 2, 8, 22, 7, 2, 23, 24, 25, 9, 12, 2, 26, 14, 27, 6, 7, 2, 28, 2, 7, 15, 29, 2, 17, 2, 12, 9, 7, 2, 30, 2, 7, 14, 8, 2, 21, 2, 31, 32, 7, 2, 33, 2, 7, 9, 34, 2, 35, 36, 8, 6, 7, 37, 38, 2, 39, 22, 40, 2, 17, 2, 41, 22

Offset: 1

Author

Antti Karttunen, Aug 24 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A009195(n), A326193(n)].

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A300242(i) = A300242(j),

a(i) = a(j) => A326196(i) = A326196(j).

Links

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

Crossrefs

Cf. A009194, A009195, A300242, A305800, A326193, A326194, A326196.

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; };
Aux326192(n) = { my(u=gcd(n,sigma(n))); [gcd(n,eulerphi(n)), u*((-1)^(u==n))]; };
v326192 = rgs_transform(vector(up_to, n, Aux326192(n)));
A326192(n) = v326192[n];