cp's OEIS Frontend

A329353 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329352(i) = A329352(j) for all i, j.

%I A329353 #7 Nov 12 2019 19:20:28
%S A329353 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,12,18,19,2,
%T A329353 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,7,34,35,25,2,36,
%U A329353 27,37,38,39,2,40,2,41,42,43,44,45,2,46,47,48,2,49,2,50,51,52,53,54,2,55,56,57,2,58,59,60,61,62,2,63,64,65,66,67,68,69,2,70,71,72,2,73,2,49,74
%N A329353 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329352(i) = A329352(j) for all i, j.
%C A329353 Restricted growth sequence transform of A329352.
%C A329353 For all i, j:
%C A329353   A305800(i) = A305800(j) => a(i) = a(j),
%C A329353   a(i) = a(j) => A069359(i) = A069359(j).
%H A329353 Antti Karttunen, <a href="/A329353/b329353.txt">Table of n, a(n) for n = 1..65537</a>
%o A329353 (PARI)
%o A329353 up_to = 65537;
%o A329353 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 A329353 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A329353 A329352(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A019565(d))); (m); };
%o A329353 v329353 = rgs_transform(vector(up_to, n, A329352(n)));
%o A329353 A329353(n) = v329353[n];
%Y A329353 Cf. A010051, A019565, A069359, A305800, A329352.
%Y A329353 Cf. also A329351.
%Y A329353 Differs from A319682 for the first time at n=254, where a(254)=123, while A319682(254)=184.
%K A329353 nonn
%O A329353 1,2
%A A329353 _Antti Karttunen_, Nov 12 2019