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Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A003557(n), A023900(n), A063994(n)].
4

%I #8 Jan 13 2019 19:30:03

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,28,29,30,31,32,33,34,35,36,37,38,35,39,40,41,42,43,44,45,46,47,48,

%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,76,92

%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A003557(n), A023900(n), A063994(n)].

%C For all i, j: a(i) = a(j) => A247074(i) = A247074(j).

%H Antti Karttunen, <a href="/A323404/b323404.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 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); };

%o A023900(n) = sumdivmult(n, d, d*moebius(d)); \\ From A023900

%o A063994(n) = { my(f=factor(n)[, 1]); prod(i=1, #f, gcd(f[i]-1, n-1)); }; \\ From A063994

%o Aux323404(n) = if(1,[A003557(n), A023900(n), A063994(n)]);

%o v323404 = rgs_transform(vector(up_to, n, Aux323404(n)));

%o A323404(n) = v323404[n];

%Y Cf. A000010, A003557, A023900, A063994, A247074, A323405.

%Y Cf. also A323373.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 13 2019