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A323366 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A173557(i) = A173557(j).

%I A323366 #7 Jan 12 2019 20:46:38
%S A323366 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,13,21,22,23,24,25,
%T A323366 26,27,28,29,30,31,32,33,34,35,36,37,34,38,39,25,40,41,42,43,44,45,46,
%U A323366 47,48,49,50,51,39,52,36,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,56,65,72,73,74,75,76,49,77,78,79,80,81,82,68,83,56,84,68,85,86,87,88,89,90,91,92,93,60
%N A323366 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A000035(i) = A000035(j) and A003557(i) = A003557(j) and A173557(i) = A173557(j).
%C A323366 For all i, j:
%C A323366   a(i) = a(j) => A007814(i) = A007814(j),
%C A323366   a(i) = a(j) => A295887(i) = A295887(j),
%C A323366   a(i) = a(j) => A323237(i) = A323237(j).
%H A323366 Antti Karttunen, <a href="/A323366/b323366.txt">Table of n, a(n) for n = 1..65537</a>
%o A323366 (PARI)
%o A323366 up_to = 65537;
%o A323366 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 A323366 A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A323366 A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557
%o A323366 v323366 = rgs_transform(vector(up_to, n, [(n%2), A003557(n), A173557(n)]));
%o A323366 A323366(n) = v323366[n];
%Y A323366 Cf. A000035, A003557, A007814, A173557, A291756, A295887, A323237, A323367.
%Y A323366 Cf. also A323368.
%K A323366 nonn
%O A323366 1,2
%A A323366 _Antti Karttunen_, Jan 12 2019