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A378605 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A033630(i) = A033630(j), for all i, j >= 1.

%I A378605 #6 Dec 01 2024 19:54:55
%S A378605 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 A378605 21,2,22,11,23,19,24,2,25,26,27,2,28,2,29,30,31,2,32,7,33,34,35,2,36,
%U A378605 26,37,38,39,2,40,2,41,42,43,44,45,2,46,47,48,2,49,2,29,50,51,44,52,2,53,29,54,2,55,38,35,30,56,2,57,34,58,59,60,61,62,2,63,64,65,2,66,2,67,68
%N A378605 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A033630(i) = A033630(j), for all i, j >= 1.
%C A378605 Restricted growth sequence transform of the ordered pair [A001065(n), A033630(n)].
%H A378605 Antti Karttunen, <a href="/A378605/b378605.txt">Table of n, a(n) for n = 1..100000</a>
%o A378605 (PARI)
%o A378605 up_to = 100000;
%o A378605 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 A378605 A001065(n) = (sigma(n)-n);
%o A378605 v033630 = readvec("b033630_to.txt"); \\ Precomputed with A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
%o A378605 A033630(n) = v033630[n];
%o A378605 Aux378605(n) = [A001065(n), A033630(n)];
%o A378605 v378605 = rgs_transform(vector(up_to, n, Aux378605(n)));
%o A378605 A378605(n) = v378605[n];
%Y A378605 Cf. A001065, A033630.
%Y A378605 Cf. also A378603.
%K A378605 nonn
%O A378605 1,2
%A A378605 _Antti Karttunen_, Dec 01 2024