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A374033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A373985(i)) = A278226(A373985(j)), for all i, j >= 1.

%I A374033 #10 Jun 27 2024 10:20:42
%S A374033 1,1,1,2,1,2,1,1,2,2,1,1,1,2,3,3,1,1,1,1,3,2,1,2,2,2,4,1,1,1,1,1,2,2,
%T A374033 2,5,1,2,2,2,1,1,1,1,1,2,1,1,2,1,3,1,1,2,6,7,3,2,1,8,1,2,1,2,6,1,1,1,
%U A374033 2,1,1,4,1,2,1,1,6,1,1,1,7,2,1,9,2,2,3,2,1,2,6,1,3,2,2,5,1,1,10,5,1,1,1,2,1
%N A374033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A373985(i)) = A278226(A373985(j)), for all i, j >= 1.
%C A374033 Restricted growth sequence transform of A278226(A373985(n)).
%C A374033 For all i, j >= 1:
%C A374033   A305800(i) = A305800(j) => a(i) = a(j) => A373989(i) = A373989(j).
%H A374033 Antti Karttunen, <a href="/A374033/b374033.txt">Table of n, a(n) for n = 1..100000</a>
%H A374033 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A374033 (PARI)
%o A374033 up_to = 100000;
%o A374033 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 A374033 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A374033 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A374033 A278226(n) = A046523(A276086(n));
%o A374033 A373985(n) = { my(f=factor(n),m=1,s=0); for(i=1, #f~, my(x=prod(i=1,primepi(f[i, 1]),prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); gcd(m,s); };
%o A374033 v374033 = rgs_transform(vector(up_to, n, A278226(A373985(n))));
%o A374033 A374033(n) = v374033[n];
%Y A374033 Cf. A002110, A046523, A108951, A276086, A278226, A373158, A373985.
%Y A374033 Cf. A305800, A373989.
%Y A374033 Cf. also A373982, A373983, A374032.
%K A374033 nonn
%O A374033 1,4
%A A374033 _Antti Karttunen_, Jun 27 2024