A328576 - OEIS

%I #6 Oct 20 2019 21:45:54

%S 1,2,2,2,3,4,2,2,2,2,3,4,3,5,5,5,6,7,8,9,9,9,10,11,12,13,13,13,14,15,

%T 2,2,2,2,3,4,2,2,2,2,3,4,3,5,5,5,6,7,8,9,9,9,10,11,12,13,13,13,14,15,

%U 3,16,16,16,17,18,16,16,16,16,17,18,17,19,19,19,20,21,22,23,23,23,24,25,26,27,27,27,28,29,30,31,31,31,32,33,31,31,31,31,32,33

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)], for all i, j.

%C Restricted growth sequence transform of function f, defined as: f(0) = 0 and for n > 0, f(n) = [A276088(n), A328575(n)].

%C For all i, j: a(i) = a(j) => A328114(i) = A328114(j).

%H Antti Karttunen, <a href="/A328576/b328576.txt">Table of n, a(n) for n = 0..32768</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%o (PARI)

%o up_to = 32768;

%o 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 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557

%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };

%o A328575(n) = A003557(A032742(A276086(n)));

%o Aux328576(n) = if(!n,n,[A276088(n), A328575(n)]);

%o v328576 = rgs_transform(vector(1+up_to, n, Aux328576(n-1)));

%o A328576(n) = v328576[1+n];

%Y Cf. A003557, A032742, A276086, A276088, A328114, A328575, A328577.

%K nonn

%O 0,2

%A _Antti Karttunen_, Oct 20 2019