A324532 - OEIS

%I #6 Mar 05 2019 18:20:19

%S 1,2,3,2,3,4,5,2,6,7,5,6,5,8,9,2,3,10,5,11,5,12,13,6,14,15,9,16,13,17,

%T 18,2,3,6,5,19,5,12,13,20,5,21,13,22,23,17,18,6,14,21,24,25,13,26,27,

%U 14,24,28,18,29,18,30,31,2,3,32,5,6,5,33,13,34,5,35,13,36,13,37,18,38,14,14,13,39,40,41,18,42,13,43,27,44,18,45,46,6,5,36,23,47,13

%N Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A000120(n), A318458(n)] for all other numbers, except f(1) = 0.

%H Antti Karttunen, <a href="/A324532/b324532.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F For n >= 1, a(2^n) = 2.

%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 A318458(n) = bitand(n,sigma(n)-n);

%o Aux324532(n) = if(1==n,0,[hammingweight(n), A318458(n)]);

%o v324532 = rgs_transform(vector(up_to,n,Aux324532(n)));

%o A324532(n) = v324532[n];

%Y Cf. A000120, A318458, A324530, A324531.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 05 2019