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A324531 Lexicographically earliest sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A318458(n)] for all other numbers, except f(1) = 0.

%I A324531 #5 Mar 05 2019 18:20:12
%S A324531 1,2,3,2,4,5,6,2,7,8,9,10,9,11,12,2,4,13,9,14,15,16,17,10,18,19,20,21,
%T A324531 17,22,23,2,4,7,9,24,15,16,17,25,15,26,27,28,29,30,31,10,18,32,33,34,
%U A324531 27,35,36,37,38,39,40,41,31,42,43,2,4,44,9,7,15,45,17,46,15,47,27,48,27,49,31,50,51,51,27,52,53,54,55,56,27,57,58,59,55,60,61,10,9,48
%N A324531 Lexicographically earliest sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A318458(n)] for all other numbers, except f(1) = 0.
%C A324531 For all i, j:
%C A324531   a(i) = a(j) => A324532(i) = A324532(j).
%H A324531 Antti Karttunen, <a href="/A324531/b324531.txt">Table of n, a(n) for n = 1..65537</a>
%H A324531 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324531 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324531 For n >= 1, a(2^n) = 2.
%o A324531 (PARI)
%o A324531 up_to = 65537;
%o A324531 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 A324531 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of _M. F. Hasler_
%o A324531 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A324531 A278222(n) = A046523(A005940(1+n));
%o A324531 A318458(n) = bitand(n,sigma(n)-n);
%o A324531 Aux324531(n) = if(1==n,0,[A278222(n), A318458(n)]);
%o A324531 v324531 = rgs_transform(vector(up_to,n,Aux324531(n)));
%o A324531 A324531(n) = v324531[n];
%Y A324531 Cf. A278222, A318458, A324400, A324530, A324532.
%K A324531 nonn
%O A324531 1,2
%A A324531 _Antti Karttunen_, Mar 05 2019