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A373268 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A373145(i) = A373145(j), for all i, j >= 1.

%I A373268 #7 Jun 09 2024 15:31:26
%S A373268 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A373268 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A373268 28,40,41,21,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,46,55,2,56,57,58,2,59,41,60,61,62,2,63,64,65,66,67,68,69,2,70,71,72,2,73,2,74,55
%N A373268 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A373145(i) = A373145(j), for all i, j >= 1.
%C A373268 Restricted growth sequence transform of the triple [A003415(n), A085731(n), A373145(n)].
%C A373268 For all i, j >= 1:
%C A373268   A373150(i) = A373150(j) => a(i) = a(j),
%C A373268   a(i) = a(j) => A373151(i) = A373151(j) => A373485(i) = A373485(j),
%C A373268   a(i) = a(j) => A373152(i) = A373152(j),
%C A373268   a(i) = a(j) => A373486(i) = A373486(j).
%H A373268 Antti Karttunen, <a href="/A373268/b373268.txt">Table of n, a(n) for n = 1..100000</a>
%o A373268 (PARI)
%o A373268 up_to = 100000;
%o A373268 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 A373268 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373268 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
%o A373268 Aux373268(n) = { my(d=A003415(n)); [d, gcd(d,n), gcd(d, A276085(n))]; };
%o A373268 v373268 = rgs_transform(vector(up_to, n, Aux373268(n)));
%o A373268 A373268(n) = v373268[n];
%Y A373268 Cf. A003415, A083345, A085731, A276085, A373145.
%Y A373268 Cf. A373150, A373151, A373152, A373485, A373486.
%Y A373268 Differs from A344025 and A369046 for the first time at n=91, where a(91) = 64, while A344025(91) = A369046(91) = 37.
%Y A373268 Differs from A351236 for the first time at n=143, where a(143) = 100, while A351236(143) = 68.
%K A373268 nonn
%O A373268 1,2
%A A373268 _Antti Karttunen_, Jun 09 2024