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A374479 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A343223(i) = A343223(j), for all i, j >= 1.

%I A374479 #7 Aug 07 2024 15:12:41
%S A374479 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 A374479 21,2,22,11,23,19,24,2,13,25,26,2,27,2,28,29,30,2,31,7,32,33,34,2,35,
%U A374479 25,36,37,38,2,39,2,40,41,42,43,44,2,45,46,47,2,48,2,49,50,51,52,53,2,54,55,56,2,57,37,58,59,60,2,61,12,62,63,26,64,65,2,66,67
%N A374479 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A343223(i) = A343223(j), for all i, j >= 1.
%C A374479 Restricted growth sequence transform of the ordered pair [A001065(n), A343223(n)].
%H A374479 Antti Karttunen, <a href="/A374479/b374479.txt">Table of n, a(n) for n = 1..65537</a>
%H A374479 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A374479 (PARI)
%o A374479 up_to = 65537;
%o A374479 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 A374479 A001065(n) = (sigma(n)-n);
%o A374479 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A374479 A342926(n) = (A003415(sigma(n))-n);
%o A374479 A343223(n) = gcd(A003415(n), A342926(n));
%o A374479 Aux374479(n) = [A001065(n), A343223(n)];
%o A374479 v374479 = rgs_transform(vector(up_to, n, Aux374479(n)));
%o A374479 A374479(n) = v374479[n];
%Y A374479 Cf. A000203, A001065, A342926, A343223.
%Y A374479 Cf. also A305800, A374480.
%K A374479 nonn
%O A374479 1,2
%A A374479 _Antti Karttunen_, Aug 07 2024