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A361026 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.

%I A361026 #7 Mar 04 2023 17:08:36
%S A361026 1,2,1,3,1,4,1,5,6,2,1,7,1,2,1,8,1,9,1,3,1,2,1,10,11,2,12,3,1,13,1,14,
%T A361026 1,2,1,15,1,2,1,5,1,4,1,3,6,2,1,16,17,18,1,3,1,19,1,5,1,2,1,20,1,2,6,
%U A361026 21,1,4,1,3,1,2,1,22,1,2,11,3,1,4,1,8,23,2,1,7,1,2,1,5,1,24,1,3,1,2,1,25,1,26,6,27,1,4,1,5,1
%N A361026 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.
%C A361026 Restricted growth sequence transform of the ordered pair [A003557(n), A053669(n)].
%C A361026 For all i, j >= 1,
%C A361026   A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),
%C A361026   a(i) = a(j) => A007814(i) = A007814(j).
%H A361026 Antti Karttunen, <a href="/A361026/b361026.txt">Table of n, a(n) for n = 1..100000</a>
%o A361026 (PARI)
%o A361026 up_to = 100000;
%o A361026 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 A361026 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A361026 A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
%o A361026 Aux361026(n) = [A003557(n), A053669(n)];
%o A361026 v361026 = rgs_transform(vector(up_to,n,Aux361026(n)));
%o A361026 A361026(n) = v361026[n];
%Y A361026 Cf. A003557, A007814, A053669.
%Y A361026 Cf. A305801, A353520.
%K A361026 nonn
%O A361026 1,2
%A A361026 _Antti Karttunen_, Mar 03 2023