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A353521 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A000035(i) = A000035(j), for all i, j >= 1.

%I A353521 #9 Apr 27 2022 20:01:26
%S A353521 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,19,20,21,
%T A353521 3,22,3,23,24,25,26,27,3,28,29,30,3,31,3,32,33,34,3,35,36,37,38,39,3,
%U A353521 40,29,41,42,22,3,43,3,44,45,46,47,48,3,49,50,51,3,52,3,53,54,55,47,56,3,57,58,59,3,60,42,61,62,63,3,64,38
%N A353521 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A000035(i) = A000035(j), for all i, j >= 1.
%C A353521 Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A000035(n)].
%C A353521 For all i, j:
%C A353521   A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),
%C A353521   a(i) = a(j) => A007814(i) = A007814(j),
%C A353521   a(i) = a(j) => A344025(i) = A344025(j),
%C A353521   a(i) = a(j) => A353522(i) = A353522(j).
%H A353521 Antti Karttunen, <a href="/A353521/b353521.txt">Table of n, a(n) for n = 1..65537</a>
%o A353521 (PARI)
%o A353521 up_to = 65537;
%o A353521 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 A353521 A000035(n) = (n%2);
%o A353521 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A353521 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A353521 Aux353521(n) = [A003415(n), A003557(n), A000035(n)];
%o A353521 v353521 = rgs_transform(vector(up_to,n,Aux353521(n)));
%o A353521 A353521(n) = v353521[n];
%Y A353521 Cf. A000035, A003415, A003557, A007814.
%Y A353521 Cf. also A305801, A344025, A351260, A353520, A353522.
%K A353521 nonn
%O A353521 1,2
%A A353521 _Antti Karttunen_, Apr 27 2022