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A296089 Filter combining the sum of divisors (A000203) and 2-adic valuation of n (A007814); restricted growth sequence transform of A286460.

%I A296089 #11 Dec 07 2017 22:19:26
%S A296089 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,15,23,24,25,
%T A296089 26,27,28,29,21,30,31,32,31,33,34,35,36,37,38,39,40,41,42,29,31,43,44,
%U A296089 45,46,47,48,49,46,50,51,52,53,54,55,39,56,57,58,59,60,61,62,59,46,63,64,65,66,67,62,68,51,69,70,71,58,72,73,74,75,76,77,78,79,54,80,59,75
%N A296089 Filter combining the sum of divisors (A000203) and 2-adic valuation of n (A007814); restricted growth sequence transform of A286460.
%C A296089 This seems to be also the restricted growth sequence transform of A286359.
%C A296089 For all i, j:
%C A296089   a(i) = a(j) => A296088(i) = A296088(j).
%H A296089 Antti Karttunen, <a href="/A296089/b296089.txt">Table of n, a(n) for n = 1..65537</a>
%o A296089 (PARI)
%o A296089 up_to = 65537;
%o A296089 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 A296089 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A296089 A000203(n) = sigma(n);
%o A296089 A001511(n) = (1+valuation(n,2));
%o A296089 A286460(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n));
%o A296089 write_to_bfile(1,rgs_transform(vector(up_to,n,A286460(n))),"b296089.txt");
%Y A296089 Cf. A000203, A007814, A286359, A286460, A296088, A296090.
%K A296089 nonn
%O A296089 1,2
%A A296089 _Antti Karttunen_, Dec 07 2017