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A374478 Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j) and A364255(i) = A364255(j), for all i, j >= 1.

%I A374478 #13 Aug 07 2024 15:11:43
%S A374478 1,2,3,4,5,6,5,7,8,9,5,10,5,11,12,13,5,14,5,15,16,17,5,18,19,20,21,22,
%T A374478 5,23,5,24,25,26,27,28,5,29,30,31,5,32,5,33,34,35,5,36,37,38,39,40,5,
%U A374478 41,42,43,44,45,5,46,5,47,48,49,50,51,5,52,53,54,5,55,5,56,57,58,59,60,5,61,62,63,5,64,65,66,67,68,5,69,70,71,72,73,39,74,5,75,76,77,5
%N A374478 Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j) and A364255(i) = A364255(j), for all i, j >= 1.
%C A374478 Restricted growth sequence transform of the ordered pair [A348717(n), A364255(n)].
%C A374478 For all i, j >= 1:
%C A374478   A305900(i) = A305900(j) => a(i) = a(j),
%C A374478   a(i) = a(j) => A305891(i) = A305891(j),
%C A374478   a(i) = a(j) => A374477(i) = A374477(j).
%H A374478 Antti Karttunen, <a href="/A374478/b374478.txt">Table of n, a(n) for n = 1..65537</a>
%H A374478 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A374478 (PARI)
%o A374478 up_to = 65537;
%o A374478 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 A374478 A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
%o A374478 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A374478 A364255(n) = gcd(n, A163511(n));
%o A374478 Aux374478(n) = [A348717(n), A364255(n)];
%o A374478 v374478 = rgs_transform(vector(up_to, n, Aux374478(n)));
%o A374478 A374478(n) = v374478[n];
%Y A374478 Cf. A163511, A348717, A364255.
%Y A374478 Cf. also A305891, A305897, A364297, A364949, A365392, A365423, A374477.
%Y A374478 Differs from A374040 first at n=77, where a(77) = 59, while A374040(77) = 50.
%Y A374478 Differs from A305900 first at n=95, where a(95) = 39, while A305900(95) = 74.
%K A374478 nonn
%O A374478 1,2
%A A374478 _Antti Karttunen_, Aug 07 2024