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A373980 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A181819(n), A373247(n)], for all i, j >= 1.

%I A373980 #6 Jun 24 2024 17:10:19
%S A373980 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 A373980 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 A373980 40,29,41,42,43,3,44,3,45,46,47,48,49,3,50,51,52,3,53,3,54,55,56,48,57,3,58,59,60,3,61,42,62,63,64,3,65,38,66,67,68,69,70,3,71,72
%N A373980 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A181819(n), A373247(n)], for all i, j >= 1.
%C A373980 Restricted growth sequence transform of the quadruple [A003415(n), A085731(n), A181819(n), A373247(n)].
%C A373980 For all i, j >= 1:
%C A373980   A305801(i) = A305801(j) => a(i) = a(j),
%C A373980   a(i) = a(j) => A300249(i) = A300249(j) => A101296(i) = A101296(j),
%C A373980   a(i) = a(j) => A369051(i) = A369051(j),
%C A373980   a(i) = a(j) => A373250(i) = A373250(j).
%H A373980 Antti Karttunen, <a href="/A373980/b373980.txt">Table of n, a(n) for n = 1..100000</a>
%o A373980 (PARI)
%o A373980 up_to = 100000;
%o A373980 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 A373980 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373980 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A373980 Aux373980(n) = { my(d=A003415(n), s=A181819(n)); [d, s, gcd(n,d), n%s]; };
%o A373980 v373980 = rgs_transform(vector(up_to, n, Aux373980(n)));
%o A373980 A373980(n) = v373980[n];
%Y A373980 Cf. A003415, A085731, A181819, A373247.
%Y A373980 Cf. A101296, A300249, A305801, A369051, A373250.
%Y A373980 Differs from A353520 and A361021 first at n=130, where a(130) = 82, while A353520(130) = A361021(130) = 96.
%K A373980 nonn
%O A373980 1,2
%A A373980 _Antti Karttunen_, Jun 24 2024