%I #7 Jan 15 2024 19:19:12

%S 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 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 28,40,41,21,2,40,2,42,43,44,45,46,2,47,48,49,2,50,2,51,52,53,45,54,2,55,56,57,2,58,41,59,60,61,2,62,37

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

%C Restricted growth sequence transform of the ordered pair [A003415(n), A085731(n)], or equally, of the pair [A003415(n), A083345(n)], or equally, of the pair [A083345(n), A085731(n)].

%C For all i, j: A369050(i) = A369050(j) => A344025(i) = A344025(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A369051/b369051.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A085731(n) = gcd(A003415(n),n);

%o Aux369051(n) = [A003415(n), A085731(n)];

%o v369051 = rgs_transform(vector(up_to, n, Aux369051(n)));

%o A369051(n) = v369051[n];

%Y Cf. A003415, A083345, A085731.

%Y Cf. also A344025, A369050.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 15 2024