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A373251 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j), i mod A181819(i) = j mod 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 A373251 #6 May 30 2024 18:48:31
%S A373251 1,2,3,4,5,6,5,7,8,9,5,10,5,6,11,12,5,10,5,13,14,6,5,15,16,6,17,18,5,
%T A373251 19,5,20,14,6,21,22,5,6,23,24,5,25,5,26,27,6,5,28,29,30,23,18,5,15,31,
%U A373251 32,14,6,5,33,5,6,34,35,36,37,5,26,14,38,5,39,5,6,40,18,41,19,5,42,43,6,5,44,45,6,23,46,5,47,21,26,14,6
%N A373251 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j), i mod A181819(i) = j mod 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 A373251 Restricted growth sequence transform of the triple [A181819(n), A373247(n), A324198(n)].
%C A373251 For all i, j:
%C A373251   A305900(i) = A305900(j) => a(i) = a(j),
%C A373251   a(i) = a(j) => A373248(i) = A373248(j),
%C A373251   a(i) = a(j) => A373250(i) = A373250(j).
%H A373251 Antti Karttunen, <a href="/A373251/b373251.txt">Table of n, a(n) for n = 1..100000</a>
%o A373251 (PARI)
%o A373251 up_to = 100000;
%o A373251 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 A373251 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A373251 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 A373251 Aux373251(n) = [A181819(n), n%A181819(n), A324198(n)];
%o A373251 v373251 = rgs_transform(vector(up_to, n, Aux373251(n)));
%o A373251 A373251(n) = v373251[n];
%Y A373251 Cf. A101296, A181819, A324198, A373247, A373248, A373250.
%K A373251 nonn
%O A373251 1,2
%A A373251 _Antti Karttunen_, May 30 2024