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%I #9 Dec 03 2018 18:29:46
%S 1,2,3,4,3,5,3,6,3,7,3,8,3,3,3,9,3,5,3,10,3,7,3,11,3,3,3,7,3,7,3,12,3,
%T 3,3,13,3,3,3,14,3,5,3,2,3,7,3,15,3,3,3,7,3,7,3,2,3,7,3,16,3,3,3,17,3,
%U 7,3,3,3,7,3,18,3,3,3,3,3,7,3,19,3,7,3,20,3,3,3,8,3,3,3,2,3,3,3,21,3,3,3,5,3,7,3,2,3
%N Lexicographically earliest such sequence a that a(i) = a(j) => A322310(i) = A322310(j) for all i, j.
%C Restricted growth sequence transform of A322310.
%C For all i, j: a(i) = a(j) => A014197(i) = A014197(j).
%H Antti Karttunen, <a href="/A322311/b322311.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A320000sq(n, k) = if(1==n, if(1==k,2,1), sumdiv(n, d, if(d>=k && isprime(d+1), my(p=d+1, q=n/d); sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))))); \\ Cf. A320000
%o A322310(n) = if(1==n,3,my(m=1); fordiv(n,d, my(s, p=d+1, q=n/d); if(isprime(p) && (s = sum(i=0,valuation(n, p), A320000sq(q/(p^i),p))), m *= prime(s))); (m));
%o v322311 = rgs_transform(vector(up_to, n, A322310(n)));
%o A322311(n) = v322311[n];
%Y Cf. A014197, A320000, A322310, A322313.
%K nonn
%O 1,2
%A _Antti Karttunen_, Dec 03 2018