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A374480 Lexicographically earliest infinite sequence such that a(i) = a(j) => A083345(i) = A083345(j) and A343223(i) = A343223(j), for all i, j >= 1.

%I A374480 #6 Aug 06 2024 16:38:28
%S A374480 1,2,2,2,2,3,2,4,5,6,2,7,2,8,9,10,2,6,2,11,12,13,2,14,5,15,2,16,2,17,
%T A374480 2,18,19,20,21,22,2,23,24,25,2,26,2,27,28,29,2,30,10,31,32,19,2,33,24,
%U A374480 34,35,17,2,34,2,36,25,37,38,39,2,38,40,41,2,13,2,42,43,44,45,46,2,43,47,48,2,49,35,50,51,52,2,53,54,55,56,57,58,59,2,43,60,61
%N A374480 Lexicographically earliest infinite sequence such that a(i) = a(j) => A083345(i) = A083345(j) and A343223(i) = A343223(j), for all i, j >= 1.
%C A374480 Restricted growth sequence transform of the ordered pair [A083345(n), A343223(n)].
%H A374480 Antti Karttunen, <a href="/A374480/b374480.txt">Table of n, a(n) for n = 1..65537</a>
%o A374480 (PARI)
%o A374480 up_to = 65537;
%o A374480 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 A374480 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A374480 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A374480 A342926(n) = (A003415(sigma(n))-n);
%o A374480 A343223(n) = gcd(A003415(n), A342926(n));
%o A374480 Aux374480(n) = [A083345(n), A343223(n)];
%o A374480 v374480 = rgs_transform(vector(up_to, n, Aux374480(n)));
%o A374480 A374480(n) = v374480[n];
%Y A374480 Cf. A003415, A083345, A342926, A343223.
%Y A374480 Cf. also A305800, A373151, A374131.
%K A374480 nonn
%O A374480 1,2
%A A374480 _Antti Karttunen_, Aug 06 2024