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A332826 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A332824(i)) = A046523(A332824(j)) for all i, j.

%I A332826 #8 Feb 25 2020 18:34:12
%S A332826 1,2,3,4,3,5,6,7,7,5,6,8,6,9,10,11,3,12,6,13,13,9,10,14,7,9,15,16,10,
%T A332826 17,18,19,19,5,19,20,6,9,19,21,6,22,10,23,24,17,18,25,19,12,10,23,10,
%U A332826 26,19,27,19,17,18,28,18,29,30,31,19,32,6,13,33,32,10,34,6,9,33,23,35,32,18,36,37,9,10,38,10,17,33,39,10,40,41,39,42,29,43,44,6,32,39,45,10,17,18,39,39
%N A332826 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A332824(i)) = A046523(A332824(j)) for all i, j.
%H A332826 Antti Karttunen, <a href="/A332826/b332826.txt">Table of n, a(n) for n = 1..65537</a>
%o A332826 (PARI)
%o A332826 up_to = 65537;
%o A332826 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 A332826 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A332826 A332824(n) = { my(m=1); fordiv(n,d,m *= A019565(eulerphi(d))); (m); };
%o A332826 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A332826 v332826 = rgs_transform(vector(up_to,n,A046523(A332824(n))));
%o A332826 A332826(n) = v332826[n];
%Y A332826 Cf. A000010, A019565, A046523, A332824, A332827.
%Y A332826 Cf. A019434 (positions of 3's).
%Y A332826 Cf. also A318835.
%K A332826 nonn
%O A332826 1,2
%A A332826 _Antti Karttunen_, Feb 25 2020