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A328474 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A276156(i)) = A046523(A276156(j)) for all i, j.

%I A328474 #5 Oct 18 2019 21:27:58
%S A328474 1,2,2,3,2,4,5,6,2,7,3,8,2,3,3,9,2,10,3,11,3,3,3,12,2,10,7,6,3,13,3,
%T A328474 14,2,15,10,16,3,6,3,17,2,3,6,9,2,10,18,19,2,6,10,6,10,20,10,21,2,22,
%U A328474 6,23,2,3,3,24,3,18,16,16,10,6,9,17,3,3,6,6,3,10,16,25,2,3,6,16,6,22,10,9,2,26,3,27,6,3,3,28,2,6,3,22,3,10,6,14,2
%N A328474 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A276156(i)) = A046523(A276156(j)) for all i, j.
%H A328474 Antti Karttunen, <a href="/A328474/b328474.txt">Table of n, a(n) for n = 1..65537</a>
%H A328474 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A328474 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328474 (PARI)
%o A328474 up_to = 65537;
%o A328474 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 A328474 A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
%o A328474 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A328474 v328474 = rgs_transform(vector(up_to, n, A046523(A276156(n))));
%o A328474 A328474(n) = v328474[n];
%Y A328474 Cf. A002110, A276156, A328461, A328471, A328473.
%K A328474 nonn
%O A328474 1,2
%A A328474 _Antti Karttunen_, Oct 18 2019