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A373379 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A107463(i) = A107463(j), for all i, j >= 1.

%I A373379 #9 Jun 06 2024 08:45:23
%S A373379 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A373379 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A373379 28,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,47,56,2,57,58,59,2,60,41,61,62,63,2,64,37,65,66,67,68,69,2,70,71,72
%N A373379 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A107463(i) = A107463(j), for all i, j >= 1.
%C A373379 Restricted growth sequence transform of the triple [A003415(n), A085731(n), A107463(n)].
%C A373379 For all i, j >= 1:
%C A373379   A305800(i) = A305800(j) => a(i) = a(j),
%C A373379   a(i) = a(j) => A369051(i) = A369051(j),
%C A373379   a(i) = a(j) => A373363(i) = A373363(j),
%C A373379   a(i) = a(j) => A373364(i) = A373364(j).
%C A373379 Starts to differ from A300235 at n=153. - _R. J. Mathar_, Jun 06 2024
%H A373379 Antti Karttunen, <a href="/A373379/b373379.txt">Table of n, a(n) for n = 1..100000</a>
%o A373379 (PARI)
%o A373379 up_to = 100000;
%o A373379 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 A373379 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373379 A085731(n) = gcd(A003415(n),n);
%o A373379 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
%o A373379 A107463(n) = if(n<=1,n,if(isprime(n),1,A001414(n)));
%o A373379 Aux373379(n) = [A003415(n), A085731(n), A107463(n)];
%o A373379 v373379 = rgs_transform(vector(up_to, n, Aux373379(n)));
%o A373379 A373379(n) = v373379[n];
%Y A373379 Cf. A001414, A003415, A085731, A107463, A305800, A369051, A373363, A373364.
%Y A373379 Differs from A305895, A327931, and A353560 for the first time at n=1610, where a(1610) = 1112, while A305895(1610) = A327931(1610) = A353560(1610) = 1210.
%Y A373379 Cf. also A373150, A373152, A373380.
%K A373379 nonn
%O A373379 1,2
%A A373379 _Antti Karttunen_, Jun 03 2024