cp's OEIS Frontend

A328629 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328627(i)) = A046523(A328627(j)) for all i, j.

%I A328629 #5 Oct 25 2019 18:08:30
%S A328629 1,2,2,3,4,5,2,5,6,7,8,9,4,3,5,10,11,12,13,6,14,15,3,16,17,14,3,18,19,
%T A328629 15,2,5,5,15,3,12,14,16,18,20,21,22,23,24,16,25,26,27,19,18,28,29,10,
%U A328629 30,31,28,24,32,33,34,4,3,3,7,8,15,5,12,28,32,33,30,19,18,12,35,36,37,31,28,38,39,15,40,41,38,18,25,26,22,13,6,6,18,19,9,42
%N A328629 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328627(i)) = A046523(A328627(j)) for all i, j.
%C A328629 Restricted growth sequence transform of function f(n) = A046523(A328627(n)), or equally, of function g(n) = A278226(A328626(n)).
%H A328629 Antti Karttunen, <a href="/A328629/b328629.txt">Table of n, a(n) for n = 0..32768</a>
%H A328629 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328629 (PARI)
%o A328629 up_to = 32768;
%o A328629 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 A328629 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A328629 A328627(n) = { my(m=1, p=2, d=0); while(n, d = lift(Mod(n,p)/(d+1)); m *= (p^d); n = n\p; p = nextprime(1+p)); (m); };
%o A328629 Aux328629(n) = A046523(A328627(n));
%o A328629 v328629 = rgs_transform(vector(1+up_to, n, Aux328629(n-1)));
%o A328629 A328629(n) = v328629[1+n];
%Y A328629 Cf. A046523, A278226, A328626, A328627, A328628.
%K A328629 nonn
%O A328629 0,2
%A A328629 _Antti Karttunen_, Oct 25 2019