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A332900 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 1 and n is a square or twice square, with f(n) = n for all other numbers.

%I A332900 #8 Mar 06 2020 11:43:25
%S A332900 1,2,3,2,4,5,6,2,2,7,8,9,10,11,12,2,13,2,14,15,16,17,18,19,2,20,21,22,
%T A332900 23,24,25,2,26,27,28,2,29,30,31,32,33,34,35,36,37,38,39,40,2,2,41,42,
%U A332900 43,44,45,46,47,48,49,50,51,52,53,2,54,55,56,57,58,59,60,2,61,62,63,64,65,66,67,68,2,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,2,85,2
%N A332900 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 1 and n is a square or twice square, with f(n) = n for all other numbers.
%C A332900 For all i, j:
%C A332900   A324400(i) = A324400(j) => a(i) = a(j),
%C A332900   a(i) = a(j) => A292383(i) = A292383(j) => A292583(i) = A292583(j),
%C A332900   a(i) = a(j) => A332896(i) = A332896(j) => A332901(i) = A332901(j).
%H A332900 Antti Karttunen, <a href="/A332900/b332900.txt">Table of n, a(n) for n = 1..65537</a>
%o A332900 (PARI)
%o A332900 up_to = 65537;
%o A332900 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 A332900 A332900aux(n) = if((n>1)&&(issquare(n)||issquare(2*n)),0,n);
%o A332900 v332900 = rgs_transform(vector(up_to,n,A332900aux(n)));
%o A332900 A332900(n) = v332900[n];
%Y A332900 Cf. A292383, A292583, A324400, A332896, A332901.
%K A332900 nonn
%O A332900 1,2
%A A332900 _Antti Karttunen_, Mar 05 2020