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%I #5 Nov 22 2018 18:17:05
%S 1,2,3,3,3,3,3,4,4,3,3,5,3,3,5,6,3,4,3,5,5,3,3,7,4,3,6,5,3,5,3,8,5,3,
%T 5,7,3,3,5,7,3,5,3,5,7,3,3,9,4,4,5,5,3,6,5,7,5,3,3,10,3,3,7,11,5,5,3,
%U 5,5,5,3,12,3,3,7,5,5,5,3,9,8,3,3,10,5,3,5,7,3,7,5,5,5,3,5,13,3,4,7,7,3,5,3,7,10
%N Restricted growth sequence transform of function f: f(1) = 0, f(n) = A046523(A252463(n)) for n > 1.
%C For all i, j: a(i) = a(j) => A320111(i) = A320111(j).
%H Antti Karttunen, <a href="/A320110/b320110.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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A252463(n) = if(!(n%2),n/2,A064989(n));
%o A320110aux(n) = if(1==n,0,A046523(A252463(n)));
%o v320110 = rgs_transform(vector(up_to,n,A320110aux(n)));
%o A320110(n) = v320110[n];
%Y Cf. A046523, A252463, A320111.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 22 2018
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