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A300235 Restricted growth sequence transform of A291765, filter combining A001065(n) and A046523(n), the sum of proper divisors and the prime signature of n.

%I A300235 #7 Mar 01 2018 14:53:33
%S A300235 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A300235 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A300235 28,40,41,42,2,43,2,44,45,46,47,48,2,49,50,51,2,52,2,53,54,55,47,56,2,57,58,59,2,60,41,61,62,63,2,64,37,65,66,67,68,69,2,70,71
%N A300235 Restricted growth sequence transform of A291765, filter combining A001065(n) and A046523(n), the sum of proper divisors and the prime signature of n.
%H A300235 Antti Karttunen, <a href="/A300235/b300235.txt">Table of n, a(n) for n = 1..65537</a>
%e A300235 a(51) = a(91) (= 33) because both are nonsquare semiprimes (3*17 and 7*13), and the sum of their proper divisors (A001065) are equal 1+3+17 = 1+7+13 = 21.
%o A300235 (PARI)
%o A300235 up_to = 65537;
%o A300235 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 A300235 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300235 A001065(n) = (sigma(n)-n);
%o A300235 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A300235 A291765(n) = (1/2)*(2 + ((A001065(n)+A046523(n))^2) - A001065(n) - 3*A046523(n));
%o A300235 write_to_bfile(1,rgs_transform(vector(up_to,n,A291765(n))),"b300235.txt");
%Y A300235 Cf. A001065, A046523, A291765.
%Y A300235 Cf. also A295885, A300223, A300226, A300229, A300230, A300231, A300232, A300233.
%K A300235 nonn
%O A300235 1,2
%A A300235 _Antti Karttunen_, Mar 01 2018