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Lexicographically earliest sequence such that a(i) = a(j) => A000203(i) = A000203(j) and A009194(i) = A009194(j) for all i, j.
3

%I #6 May 08 2019 22:19:02

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,16,20,

%T 25,26,27,28,21,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,32,44,45,

%U 46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,51,67,68,69,70,71,72,73,53,74,75,64,61,76,77,78,79,80,81,82,83,84,85,66

%N Lexicographically earliest sequence such that a(i) = a(j) => A000203(i) = A000203(j) and A009194(i) = A009194(j) for all i, j.

%C Restricted growth sequence transform of the ordered pair [A000203(n), A009194(n)].

%H Antti Karttunen, <a href="/A325383/b325383.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</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 A009194(n) = gcd(n,sigma(n));

%o v325383 = rgs_transform(vector(up_to,n,[sigma(n),A009194(n)]));

%o A325383(n) = v325383[n];

%Y Cf. A000203, A009194, A295300, A325381, A325384.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 08 2019