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A326200 Lexicographically earliest sequence such that a(i) = a(j) => sigma(i)/i = sigma(j)/j for all i, j.

%I A326200 #18 Aug 12 2019 23:26:10
%S A326200 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A326200 27,6,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U A326200 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90
%N A326200 Lexicographically earliest sequence such that a(i) = a(j) => sigma(i)/i = sigma(j)/j for all i, j.
%C A326200 Restricted growth sequence transform of the abundancy index of n.
%C A326200 For all i, j:
%C A326200   a(i) = a(j) <=> A094759(i) = A094759(j),
%C A326200   a(i) = a(j) => A017665(i) = A017665(j),
%C A326200   a(i) = a(j) => A017666(i) = A017666(j).
%H A326200 Antti Karttunen, <a href="/A326200/b326200.txt">Table of n, a(n) for n = 1..105664</a>
%H A326200 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>
%o A326200 (PARI)
%o A326200 up_to = 105664; \\ (In the same equivalence class as 78, 364 and 6448).
%o A326200 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 A326200 v326200 = rgs_transform(vector(up_to,n,sigma(n)/n));
%o A326200 A326200(n) = v326200[n];
%Y A326200 Cf. A000396 (positions of 6's), A005820 (positions of 119's).
%Y A326200 Cf. A017665, A017666, A074902, A094759.
%Y A326200 Cf. A218406, A218407, A218408, A218427, A326202.
%K A326200 nonn
%O A326200 1,2
%A A326200 _Antti Karttunen_, Jun 13 2019