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A328470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A053669(i) = A053669(j) for all i, j.

%I A328470 #7 Oct 19 2019 21:27:46
%S A328470 1,2,3,4,3,5,3,6,7,8,3,9,3,8,10,11,3,9,3,12,10,8,3,13,7,8,14,12,3,15,
%T A328470 3,16,10,8,10,17,3,8,10,18,3,19,3,12,20,8,3,21,7,12,10,12,3,13,10,18,
%U A328470 10,8,3,22,3,8,20,23,10,19,3,12,10,24,3,25,3,8,20,12,10,19,3,26,27,8,3,28,10,8,10,18,3,22,10,12,10,8,10,29,3,12,20,30,3,19,3,18,31
%N A328470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A053669(i) = A053669(j) for all i, j.
%C A328470 Restricted growth sequence transform of A286142, or equally, of the ordered pair [A046523(n), A053669(n)], where A053669(n) gives the smallest prime not dividing n, while A046523(n) gives the prime signature of n.
%C A328470 For all i, j:
%C A328470   A305801(i) = A305801(j) => a(i) = a(j) => A291761(i) = A291761(j).
%H A328470 Antti Karttunen, <a href="/A328470/b328470.txt">Table of n, a(n) for n = 1..100000</a>
%o A328470 (PARI)
%o A328470 up_to = 100000;
%o A328470 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 A328470 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A328470 A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
%o A328470 Aux328470(n) = [A046523(n), A053669(n)];
%o A328470 v328470 = rgs_transform(vector(up_to, n, Aux328470(n)));
%o A328470 A328470(n) = v328470[n];
%Y A328470 Cf. A046523, A053669, A286142, A291761, A305801, A328469.
%K A328470 nonn
%O A328470 1,2
%A A328470 _Antti Karttunen_, Oct 19 2019