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A322021 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(i) = A046523(j) and A048250(i) = A048250(j), for all i, j.

%I A322021 #9 Dec 02 2018 20:53:06
%S A322021 1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,12,17,18,19,20,21,22,23,24,
%T A322021 25,26,27,28,29,30,31,32,31,33,34,35,36,37,38,39,40,41,26,42,43,44,45,
%U A322021 18,42,46,47,22,42,48,49,50,51,52,53,54,55,56,57,58,59,60,54,58,61,62,63,64,26,65,54,66,67,68,69,70,71,72,73,74,75,76,77,52,78,79,80,81,75,82,83,26
%N A322021 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(i) = A046523(j) and A048250(i) = A048250(j), for all i, j.
%C A322021 Restricted growth sequence transform of A291758, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291758(i) = A291758(j) <=> A046523(i) = A046523(j) and A048250(i) = A048250(j). That this is equal to the definition given in the title follows because any such lexicographically least sequence satisfying relation <=> is also the least sequence satisfying relation => with the same parameters.
%C A322021 For all i, j:
%C A322021   A295300(i) = A295300(j) => a(i) = a(j),
%C A322021   a(i) = a(j) => A304411(i) = A304411(j),
%C A322021   a(i) = a(j) => A304412(i) = A304412(j).
%H A322021 Antti Karttunen, <a href="/A322021/b322021.txt">Table of n, a(n) for n = 1..65537</a>
%o A322021 (PARI)
%o A322021 up_to = 65537;
%o A322021 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 A322021 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A322021 A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
%o A322021 v322021 = rgs_transform(vector(up_to, n, [A046523(n), A048250(n)]));
%o A322021 A322021(n) = v322021[n];
%Y A322021 Cf. A046523, A048250, A291751, A291758, A294877, A295300, A322022.
%Y A322021 Cf. also A304411, A304412.
%K A322021 nonn
%O A322021 1,2
%A A322021 _Antti Karttunen_, Nov 29 2018