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A286605 Restricted growth sequence computed for number of divisors, d(n) (A000005).

%I A286605 #11 May 12 2017 18:22:08
%S A286605 1,2,2,3,2,4,2,4,3,4,2,5,2,4,4,6,2,5,2,5,4,4,2,7,3,4,4,5,2,7,2,5,4,4,
%T A286605 4,8,2,4,4,7,2,7,2,5,5,4,2,9,3,5,4,5,2,7,4,7,4,4,2,10,2,4,5,11,4,7,2,
%U A286605 5,4,7,2,10,2,4,5,5,4,7,2,9,6,4,2,10,4,4,4,7,2,10,4,5,4,4,4,10,2,5,5,8,2,7,2,7,7,4,2,10,2,7,4,9,2,7,4,5,5,4,4
%N A286605 Restricted growth sequence computed for number of divisors, d(n) (A000005).
%C A286605 For all i, j: A101296(i) = A101296(j) => a(i) = a(j).
%C A286605 For all i, j: a(i) = a(j) <=> A000005(i) = A000005(j).
%H A286605 Antti Karttunen, <a href="/A286605/b286605.txt">Table of n, a(n) for n = 1..10000</a>
%t A286605 With[{nn = 119}, Function[s, Table[Position[Keys@ s, k_ /; MemberQ[k, n]][[1, 1]], {n, nn}]]@ Map[#1 -> #2 & @@ # &, Transpose@ {Values@ #, Keys@ #}] &@ PositionIndex@ Array[DivisorSigma[0, #] &, nn]] (* _Michael De Vlieger_, May 12 2017, Version 10 *)
%o A286605 (PARI)
%o A286605 rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A286605 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A286605 A000005(n) = numdiv(n);
%o A286605 write_to_bfile(1,rgs_transform(vector(10000,n,A000005(n))),"b286605.txt");
%Y A286605 Cf. A000005, A007416 (positions of records, and also the first occurrence of each n).
%Y A286605 Cf. also A101296, A286603, A286610, A286619, A286621, A286622, A286626, A286378.
%K A286605 nonn
%O A286605 1,2
%A A286605 _Antti Karttunen_, May 11 2017