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A319682 Restricted growth sequence transform of A300832.

%I A319682 #8 Sep 29 2018 18:42:24
%S A319682 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,12,18,19,2,
%T A319682 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,7,34,35,25,2,36,
%U A319682 27,37,38,39,2,40,2,41,42,43,44,45,2,46,47,48,2,49,2,50,51,52,53,54,2,55,56,57,2,58,59,60,61,62,2,63,64,65,66,67,68,69,2,70,71,72,2,73,2,49
%N A319682 Restricted growth sequence transform of A300832.
%C A319682 For all i, j: a(i) = a(j) => A318320(i) = A318320(j).
%H A319682 Antti Karttunen, <a href="/A319682/b319682.txt">Table of n, a(n) for n = 1..65537</a>
%o A319682 (PARI)
%o A319682 up_to = 65537;
%o A319682 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 A319682 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A319682 A300832(n) = { my(m=1); fordiv(n,d,if(-1==moebius(n/d), m *= A019565(d))); m; };
%o A319682 v319682 = rgs_transform(vector(up_to,n,A300832(n)));
%o A319682 A319682(n) = v319682[n];
%Y A319682 Cf. A300832, A319681.
%K A319682 nonn
%O A319682 1,2
%A A319682 _Antti Karttunen_, Sep 29 2018