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A373981 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A107463(n), A181819(n), A373247(n)], for all i, j >= 1.

%I A373981 #6 Jun 24 2024 23:28:33
%S A373981 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,19,20,21,
%T A373981 3,22,3,23,24,25,26,27,3,28,29,30,3,31,3,32,33,34,3,35,36,37,38,39,3,
%U A373981 40,29,41,42,43,3,44,3,45,46,47,48,49,3,50,51,52,3,53,3,54,46,55,48,56,3,57,58,59,3,60,42,61,62,63,3,64,38,65,66,67,68,69,3,70,71
%N A373981 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A107463(n), A181819(n), A373247(n)], for all i, j >= 1.
%C A373981 Restricted growth sequence transform of the triple [A107463(n), A181819(n), A373247(n)].
%C A373981 For all i, j >= 1:
%C A373981   A305801(i) = A305801(j) => a(i) = a(j),
%C A373981   a(i) = a(j) => A373250(i) = A373250(j) => A101296(i) = A101296(j),
%C A373981   a(i) = a(j) => A373976(i) = A373976(j).
%H A373981 Antti Karttunen, <a href="/A373981/b373981.txt">Table of n, a(n) for n = 1..100000</a>
%o A373981 (PARI)
%o A373981 up_to = 100000;
%o A373981 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 A373981 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
%o A373981 A107463(n) = if(n<=1,n,if(isprime(n),1,A001414(n)));
%o A373981 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A373981 Aux373981(n) = { my(s=A181819(n)); [A107463(n), s, n%s]; };
%o A373981 v373981 = rgs_transform(vector(up_to, n, Aux373981(n)));
%o A373981 A373981(n) = v373981[n];
%Y A373981 Cf. A107463, A181819, A373247.
%Y A373981 Cf. A101296, A305801, A373250, A373976.
%Y A373981 Cf. also A373379, A373980.
%K A373981 nonn
%O A373981 1,2
%A A373981 _Antti Karttunen_, Jun 24 2024