%I #7 Oct 26 2023 13:22:14
%S 1,1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,
%T 16,1,17,9,18,5,19,10,20,3,21,11,22,6,23,12,24,2,25,13,26,7,27,14,28,
%U 4,29,15,30,8,14,16,31,1,32,17,33,9,34,18,35,5,36,19,37,10,38,20,39,3,40,21,41,11,42,22,43,6
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A324186(i) = A324186(j) for all i, j >= 0, where A324186 is the sum of odd divisors permuted by A163511.
%C Restricted growth sequence transform of A324186.
%H Antti Karttunen, <a href="/A366806/b366806.txt">Table of n, a(n) for n = 0..65537</a>
%F For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%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 A000593(n) = sigma(n>>valuation(n, 2)); \\ From A000593
%o A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A324186(n) = A000593(A163511(n));
%o v366806 = rgs_transform(vector(1+up_to,n,A324186(n-1)));
%o A366806(n) = v366806[1+n];
%Y Cf. A000265, A000593, A163511, A324186.
%Y Cf. also A366804.
%K nonn
%O 0,4
%A _Antti Karttunen_, Oct 26 2023