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A328472 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A328461(i)) = A278226(A328461(j)) for all i, j.

%I A328472 #5 Oct 18 2019 21:28:12
%S A328472 1,1,2,1,2,3,4,1,2,5,4,1,4,6,7,1,2,8,4,2,4,9,7,2,4,10,7,11,7,12,13,1,
%T A328472 2,14,4,15,4,16,7,17,4,18,7,19,7,20,13,3,4,21,7,22,7,23,13,24,7,25,13,
%U A328472 22,13,26,27,1,2,28,4,29,4,30,7,20,4,31,7,32,7,33,13,34,4,35,7,36,7,37,13,38,7,39,13,36,13,40,27,22,4
%N A328472 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A328461(i)) = A278226(A328461(j)) for all i, j.
%C A328472 Restricted growth sequence transform of function f(n) = A046523(A276086(A276156(n)/A002110(A007814(n)))).
%H A328472 Antti Karttunen, <a href="/A328472/b328472.txt">Table of n, a(n) for n = 1..65537</a>
%H A328472 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A328472 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328472 (PARI)
%o A328472 up_to = 65537;
%o A328472 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 A328472 A002110(n) = prod(i=1,n,prime(i));
%o A328472 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 A328472 A328461(n) = (A276156(n)/A002110(valuation(n,2)));
%o A328472 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A328472 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328472 A278226(n) = A046523(A276086(n));
%o A328472 v328472 = rgs_transform(vector(up_to, n, A278226(A328461(n))));
%o A328472 A328472(n) = v328472[n];
%Y A328472 Cf. A002110, A007814, A046523, A276156, A276086, A278226, A328461, A328471.
%K A328472 nonn
%O A328472 1,3
%A A328472 _Antti Karttunen_, Oct 18 2019