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A322824 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = 0 if n is an odd prime, and f(n) = A242424(n) for all other numbers.

%I A322824 #9 Dec 30 2018 07:55:39
%S A322824 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,10,14,15,3,16,17,18,19,20,
%T A322824 3,14,3,21,22,23,24,25,3,26,27,15,3,28,3,29,30,31,3,32,33,24,34,35,3,
%U A322824 36,37,29,38,39,3,22,3,40,41,42,43,44,3,45,46,33,3,47,3,48,49,50,51,52,3,18,53,54,3,44,55,56,57,58,3,59,60,61,62,63,64,65,3,66,67,37,3
%N A322824 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = 0 if n is an odd prime, and f(n) = A242424(n) for all other numbers.
%C A322824 For all i, j: a(i) = a(j) => A087436(i) = A087436(j).
%H A322824 Antti Karttunen, <a href="/A322824/b322824.txt">Table of n, a(n) for n = 1..65537</a>
%o A322824 (PARI)
%o A322824 up_to = 65537;
%o A322824 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 A322824 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A322824 A242424(n) = if(1==n,n,prime(bigomega(n))*A064989(n));
%o A322824 A322824aux(n) = if((n>2)&&isprime(n),0,A242424(n));
%o A322824 v322824 = rgs_transform(vector(up_to,n,A322824aux(n)));
%o A322824 A322824(n) = v322824[n];
%Y A322824 Cf. A087436, A242424, A322814.
%K A322824 nonn
%O A322824 1,2
%A A322824 _Antti Karttunen_, Dec 29 2018