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A323371 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A295886(n) for all other numbers, except f(n) = 0 for odd primes.

%I A323371 #10 Jan 13 2019 19:29:23
%S A323371 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,15,19,20,
%T A323371 3,21,3,22,23,24,25,26,3,27,25,28,3,29,3,30,31,32,3,33,34,35,36,37,3,
%U A323371 38,39,40,41,42,3,43,3,44,45,46,47,48,3,49,50,51,3,52,3,41,53,54,55,51,3,56,57,39,3,58,59,60,61,62,3,63,64,65,55,66,64,67,3,68,69
%N A323371 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A295886(n) for all other numbers, except f(n) = 0 for odd primes.
%C A323371 Restricted growth sequence transform of function f, defined as f(n) = 0 when n is an odd prime, and f(n) = [A003557(n), A023900(n)] for all other numbers.
%C A323371 For all i, j:
%C A323371   A323370(i) = A323370(j) => a(i) = a(j),
%C A323371   A323405(i) = A323405(j) => a(i) = a(j),
%C A323371   a(i) = a(j) => A092248(i) = A092248(j),
%C A323371   a(i) = a(j) => A319340(i) = A319340(j),
%C A323371   a(i) = a(j) => A322587(i) = A322587(j).
%H A323371 Antti Karttunen, <a href="/A323371/b323371.txt">Table of n, a(n) for n = 1..65537</a>
%o A323371 (PARI)
%o A323371 up_to = 65537;
%o A323371 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 A323371 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); };
%o A323371 A023900(n) = sumdivmult(n, d, d*moebius(d)); \\ From A023900
%o A323371 Aux323371(n) = if((n>2)&&isprime(n),0,[A003557(n), A023900(n)]);
%o A323371 v323371 = rgs_transform(vector(up_to, n, Aux323371(n)));
%o A323371 A323371(n) = v323371[n];
%Y A323371 Cf. A003557, A023900, A092248, A295886, A305801, A319340, A322587, A323370, A323405.
%K A323371 nonn
%O A323371 1,2
%A A323371 _Antti Karttunen_, Jan 13 2019