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A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.

%I A373380 #7 Jun 03 2024 10:30:33
%S A373380 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,2,2,12,13,14,2,2,13,15,16,17,2,2,
%T A373380 2,18,19,20,21,22,2,23,24,2,2,25,2,26,2,27,2,28,19,29,30,31,2,2,24,2,
%U A373380 32,33,2,3,2,34,35,36,37,2,2,12,38,2,2,39,2,40,2,41,37,42,2,28,43,44,2,45,32,46,47,2,2,2,48,26,49,50,51,2,2,2,2,52
%N A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.
%C A373380 Restricted growth sequence transform of the triple [A373145(n), A373362(n), A373364(n)], i.e., the triple [gcd(x, y), gcd(x, z), gcd(y, z)], where x=A001414(n), y=A003415(n), z=A276085(n).
%C A373380 For all i, j >= 1:
%C A373380   A305800(i) = A305800(j) => a(i) = a(j),
%C A373380   a(i) = a(j) => A373367(i) = A373367(j).
%H A373380 Antti Karttunen, <a href="/A373380/b373380.txt">Table of n, a(n) for n = 1..100000</a>
%o A373380 (PARI)
%o A373380 up_to = 100000;
%o A373380 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 A373380 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
%o A373380 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373380 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
%o A373380 Aux373380(n) = { my(x=A001414(n), y=A003415(n), z=A276085(n)); [gcd(x, y), gcd(x, z), gcd(y, z)]; };
%o A373380 v373380 = rgs_transform(vector(up_to, n, Aux373380(n)));
%o A373380 A373380(n) = v373380[n];
%Y A373380 Cf. A001414, A003415, A276085, A305800, A373145, A373362, A373364, A373367.
%Y A373380 Cf. also A373150, A373379.
%K A373380 nonn
%O A373380 1,2
%A A373380 _Antti Karttunen_, Jun 03 2024