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A324538 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A324537(n) for all other numbers, except f(1) = 0.

%I A324538 #7 Mar 07 2019 23:28:42
%S A324538 1,2,2,2,2,3,2,2,2,4,2,5,2,6,4,2,2,7,2,4,6,8,2,9,2,10,2,6,2,11,2,2,8,
%T A324538 12,6,13,2,14,10,15,2,16,2,8,15,17,2,18,2,19,12,10,2,20,8,6,14,21,2,
%U A324538 22,2,23,6,2,10,24,2,12,17,25,2,26,2,27,19,14,8,28,2,29,2,30,2,31,12,32,21,8,2,33,10,17,23,34,14,35,2,36,8,37,2,38,2,10,25
%N A324538 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A324537(n) for all other numbers, except f(1) = 0.
%C A324538 For all i, j:
%C A324538   a(i) = a(j) => A069513(i) = A069513(j),
%C A324538   a(i) = a(j) => A324191(i) = A324191(j).
%H A324538 Antti Karttunen, <a href="/A324538/b324538.txt">Table of n, a(n) for n = 1..65537</a>
%o A324538 (PARI)
%o A324538 up_to = 65537;
%o A324538 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 A324538 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A324538 A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
%o A324538 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
%o A324538 A324537(n) = { my(m=1); fordiv(n, d, if(d>2, m *= prime(A297167(d)))); A003557(m); };
%o A324538 Aux324538(n) = if(1==n,0,A324537(n));
%o A324538 v324538 = rgs_transform(vector(up_to,n,Aux324538(n)));
%o A324538 A324538(n) = v324538[n];
%Y A324538 Cf. A000961 (positions of terms <= 2), A069513, A297167, A324191, A324537.
%Y A324538 Cf. also A300827, A324181, A324203, A324196, A324197.
%K A324538 nonn
%O A324538 1,2
%A A324538 _Antti Karttunen_, Mar 07 2019