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A374485 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350388(i) = A350388(j) and A351569(i) = A351569(j), for all i, j >= 1.

%I A374485 #7 Aug 06 2024 16:38:32
%S A374485 1,2,3,4,5,6,7,8,9,10,6,11,12,13,13,14,10,15,16,17,18,19,13,20,21,22,
%T A374485 23,24,25,26,18,27,28,29,28,30,31,20,32,33,22,34,35,36,37,26,28,38,39,
%U A374485 40,26,41,29,42,26,42,43,33,20,44,45,34,46,47,48,49,50,51,34,49,26,52,53,54,55,56,34,57,43,58,59,60,48,61,62,63,42,64,33,65,66,44,67,49,42,68
%N A374485 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350388(i) = A350388(j) and A351569(i) = A351569(j), for all i, j >= 1.
%C A374485 Restricted growth sequence transform of the ordered pair [A350388(n), A351569(n)].
%C A374485 For all i, j >= 1: a(i) = a(j) => A000203(i) = A000203(j).
%H A374485 Antti Karttunen, <a href="/A374485/b374485.txt">Table of n, a(n) for n = 1..65537</a>
%H A374485 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A374485 (PARI)
%o A374485 up_to = 65537;
%o A374485 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 A374485 A350388(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(0==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };
%o A374485 A350389(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(1==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };
%o A374485 A351569(n) = sigma(A350389(n));
%o A374485 Aux374485(n) = [A350388(n), A351569(n)];
%o A374485 v374485 = rgs_transform(vector(up_to, n, Aux374485(n)));
%o A374485 A374485(n) = v374485[n];
%Y A374485 Cf. A000203, A350388, A350389, A351569.
%Y A374485 Cf. also A286603, A291751.
%K A374485 nonn
%O A374485 1,2
%A A374485 _Antti Karttunen_, Aug 06 2024