%I #13 Jan 09 2023 21:31:04

%S 1,2,2,3,4,5,2,5,3,6,7,8,4,3,9,10,3,11,12,13,5,14,15,16,17,9,13,18,19,

%T 14,2,5,5,14,3,11,3,14,6,20,21,22,7,18,23,24,18,25,26,23,16,27,28,29,

%U 30,31,32,33,34,35,4,3,3,6,19,14,9,16,10,36,37,38,39,40,41,42,40,43,13,8,11,44,10,45,26,23,46,47,21,22,12,13,13,18,7,8,48,49,40

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328624(i)) = A046523(A328624(j)) for all i, j.

%C Restricted growth sequence transform of function f(n) = A046523(A328624(n)) = A278226(A328625(n)).

%C For all i, j:

%C a(i) = a(j) => A328630(i) = A328630(j).

%C The scatter plot looks like a mound (or hive) of insects. - _Antti Karttunen_, Jan 09 2023

%H Antti Karttunen, <a href="/A328628/b328628.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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

%o A328624(n) = { my(m=1, p=2, e, g=1); while(n, e = (n%p); m *= (p^((g*e)%p)); g = e+1; n = n\p; p = nextprime(1+p)); (m); };

%o Aux328628(n) = A046523(A328624(n));

%o v328628 = rgs_transform(vector(1+up_to, n, Aux328628(n-1)));

%o A328628(n) = v328628[1+n];

%Y Cf. A046523, A278226, A328624, A328625, A328629, A328630.

%K nonn,look

%O 0,2

%A _Antti Karttunen_, Oct 25 2019