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A373248 Lexicographically earliest infinite sequence such that a(i) = a(j) => gcd(i,A181819(i)) = gcd(j,A181819(j)) and gcd(i,A276086(i)) = gcd(j,A276086(j)), for all i, j >= 1, where A181819 is the prime shadow of n, and A276086 is the primorial base exp-function.

%I A373248 #6 May 30 2024 16:58:11
%S A373248 1,2,3,1,1,2,1,1,4,5,1,6,1,2,7,1,1,6,1,5,3,2,1,2,8,2,3,2,1,2,1,1,3,2,
%T A373248 9,10,1,2,3,11,1,12,1,2,13,2,1,2,9,14,3,2,1,2,15,12,3,2,1,16,1,2,17,1,
%U A373248 1,2,1,2,3,18,1,19,1,2,20,2,9,2,1,5,3,2,1,21,15,2,3,2,1,6,9,2,3,2,1,2,1,22,4,15
%N A373248 Lexicographically earliest infinite sequence such that a(i) = a(j) => gcd(i,A181819(i)) = gcd(j,A181819(j)) and gcd(i,A276086(i)) = gcd(j,A276086(j)), for all i, j >= 1, where A181819 is the prime shadow of n, and A276086 is the primorial base exp-function.
%C A373248 Restricted growth sequence transform of the ordered pair [A324198(n), A373246(n)].
%H A373248 Antti Karttunen, <a href="/A373248/b373248.txt">Table of n, a(n) for n = 1..65537</a>
%o A373248 (PARI)
%o A373248 up_to = 65537;
%o A373248 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 A373248 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A373248 A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
%o A373248 Aux373248(n) = [gcd(n, A181819(n)), A324198(n)];
%o A373248 v373248 = rgs_transform(vector(up_to, n, Aux373248(n)));
%o A373248 A373248(n) = v373248[n];
%Y A373248 Cf. A181819, A276086, A324198, A373246.
%K A373248 nonn
%O A373248 1,2
%A A373248 _Antti Karttunen_, May 29 2024