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A300229 Restricted growth sequence transform of A285729, combining A032742(n) and A046523(n), the largest proper divisor and the prime signature of n.

%I A300229 #9 Mar 01 2018 14:52:54
%S A300229 1,2,2,3,2,4,2,5,6,7,2,8,2,9,7,10,2,11,2,12,9,13,2,14,15,16,17,18,2,
%T A300229 19,2,20,13,21,9,22,2,23,16,24,2,25,2,26,27,28,2,29,30,31,21,32,2,33,
%U A300229 13,34,23,35,2,36,2,37,38,39,16,40,2,41,28,42,2,43,2,44,31,45,13,46,2,47,48,49,2,50,21,51,35,52,2,53,16,54,37,55,23,56,2,57
%N A300229 Restricted growth sequence transform of A285729, combining A032742(n) and A046523(n), the largest proper divisor and the prime signature of n.
%H A300229 Antti Karttunen, <a href="/A300229/b300229.txt">Table of n, a(n) for n = 1..65537</a>
%e A300229 a(10) = a(15) (= 7) because both are nonsquare semiprimes (2*5 and 3*5), and when the smallest prime factor is divided out, both yield the same quotient, 5.
%o A300229 (PARI)
%o A300229 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 A300229 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300229 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A300229 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A300229 A285729(n) = (1/2)*(2 + ((A032742(n)+A046523(n))^2) - A032742(n) - 3*A046523(n));
%o A300229 write_to_bfile(1,rgs_transform(vector(65537,n,A285729(n))),"b300229.txt");
%Y A300229 Cf. A032742, A046523, A285729.
%Y A300229 Cf. also A300223, A300226, A300230, A300231, A300232, A300233, A300235.
%K A300229 nonn
%O A300229 1,2
%A A300229 _Antti Karttunen_, Mar 01 2018