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A353565 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353564(i) = A353564(j), where A353564(n) = Product_{d|n, d A276086(phi(d)).

%I A353565 #10 Apr 27 2022 20:01:45
%S A353565 1,2,2,3,2,4,2,4,5,6,2,7,2,8,9,7,2,10,2,11,12,10,2,13,14,15,12,16,2,
%T A353565 17,2,18,19,20,21,22,2,23,24,25,2,26,2,22,27,28,2,29,30,31,32,33,2,34,
%U A353565 35,36,37,26,2,38,2,39,40,41,42,43,2,44,45,46,2,47,2,48,49,50,42,51,2,52,40,53,2,54,27,55,56,47,2,57
%N A353565 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353564(i) = A353564(j), where A353564(n) = Product_{d|n, d<n} A276086(phi(d)).
%C A353565 Restricted growth sequence transform of A353564.
%C A353565 For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A051953(i) = A051953(j).
%H A353565 Antti Karttunen, <a href="/A353565/b353565.txt">Table of n, a(n) for n = 1..65537</a>
%o A353565 (PARI)
%o A353565 up_to = 65537;
%o A353565 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 A353565 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A353565 A353564(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A276086(eulerphi(d)))); m; };
%o A353565 v353565 = rgs_transform(vector(up_to,n,A353564(n)));
%o A353565 A353565(n) = v353565[n];
%Y A353565 Cf. A000010, A051953, A276086, A353563, A353564.
%Y A353565 Cf. also A305800, A318835.
%K A353565 nonn,look
%O A353565 1,2
%A A353565 _Antti Karttunen_, Apr 27 2022