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%I #6 Dec 04 2017 08:59:24
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,17,18,19,20,21,22,23,24,25,
%T 26,27,28,29,30,31,32,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
%U 48,44,49,50,51,44,51,52,53,54,55,56,57,58,59,60,61,62,63,57,61,64,65,66,67,68,69,57,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,79
%N Filter combining the number of divisors (A000005) and the sum of divisors (A000203) of n.
%H Antti Karttunen, <a href="/A295880/b295880.txt">Table of n, a(n) for n = 1..65537</a>
%F Restricted growth sequence transform of a(n) = (1/2)*(2 + ((A000005(n) + A000203(n))^2) - A000005(n) - 3*A000203(n)).
%o (PARI)
%o allocatemem(2^30);
%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 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A000005(n) = numdiv(n);
%o A000203(n) = sigma(n);
%o Anotsubmitted0(n) = (1/2)*(2 + ((A000005(n)+A000203(n))^2) - A000005(n) - 3*A000203(n));
%o write_to_bfile(1,rgs_transform(vector(up_to,n,Anotsubmitted0(n))),"b295880.txt");
%Y Cf. A000005, A000203, A295300, A295888.
%K nonn
%O 1,2
%A _Antti Karttunen_, Dec 03 2017
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