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A325980 Lexicographically earliest sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A324213(i) = A324213(j) for all i, j.

%I A325980 #6 May 31 2019 20:14:15
%S A325980 1,2,3,4,2,5,2,6,7,8,9,10,9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
%T A325980 25,26,27,14,28,23,29,30,31,26,32,33,34,35,36,26,37,15,38,39,40,41,42,
%U A325980 43,44,45,46,47,48,49,50,51,52,35,50,53,54,50,55,56,57,38,58,45,59,45,60,61,62,63,64,45,65,66,67,68,69,60,70,71,72,68,73,49,74,75,76,71
%N A325980 Lexicographically earliest sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A324213(i) = A324213(j) for all i, j.
%C A325980 Restricted growth sequence transform of the ordered pair [A046523(n), A324213(n)].
%C A325980 For all i, j: a(i) = a(j) => A325815(i) = A325815(j).
%H A325980 Antti Karttunen, <a href="/A325980/b325980.txt">Table of n, a(n) for n = 1..65537</a>
%o A325980 (PARI)
%o A325980 up_to = 65537;
%o A325980 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 A325980 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A325980 A324213(n) = { my(s=sigma(n)); sum(i=0, s, (1==gcd(n-i, n-(s-i)))); };
%o A325980 v325980 = rgs_transform(vector(up_to,n,[A046523(n), A324213(n)]));
%o A325980 A325980(n) = v325980[n];
%Y A325980 Cf. A046523, A324213, A325815.
%K A325980 nonn
%O A325980 1,2
%A A325980 _Antti Karttunen_, May 30 2019