A326192 - OEIS

%I #6 Aug 24 2019 21:28:37

%S 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,

%T 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,

%U 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

%N 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)).

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

%C For all i, j:

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

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

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

%H Antti Karttunen, <a href="/A326192/b326192.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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; };

%o Aux326192(n) = { my(u=gcd(n,sigma(n))); [gcd(n,eulerphi(n)), u*((-1)^(u==n))]; };

%o v326192 = rgs_transform(vector(up_to, n, Aux326192(n)));

%o A326192(n) = v326192[n];

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Aug 24 2019