cp's OEIS Frontend

A374040 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A007814(n), A007949(n)], for all i, j >= 1.

%I A374040 #7 Jul 01 2024 20:15:40
%S A374040 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 A374040 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 A374040 41,42,43,44,45,5,46,5,47,48,49,50,51,5,52,53,54,5,55,5,56,57,58,50,59,5,60,61,62,5,63,64,65,66,67,5,68,69,70,71,72,73,74,5,75
%N A374040 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A007814(n), A007949(n)], for all i, j >= 1.
%C A374040 Restricted growth sequence transform of the quadruple [A003415(n), A085731(n), A007814(n), A007949(n)].
%C A374040 For all i, j >= 1:
%C A374040   A305900(i) = A305900(j) => a(i) = a(j),
%C A374040   a(i) = a(j) => A322026(i) = A322026(j),
%C A374040   a(i) = a(j) => A369051(i) = A369051(j) => A083345(i) = A083345(j),
%C A374040   a(i) = a(j) => b(i) = b(j), where b can be any of the sequences listed at the crossrefs-section, under "some of the other matched sequences".
%H A374040 Antti Karttunen, <a href="/A374040/b374040.txt">Table of n, a(n) for n = 1..100000</a>
%o A374040 (PARI)
%o A374040 up_to = 100000;
%o A374040 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 A374040 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A374040 Aux374040(n) = { my(d=A003415(n)); [d, gcd(n,d), valuation(n,2), valuation(n,3)]; };
%o A374040 v374040 = rgs_transform(vector(up_to, n, Aux374040(n)));
%o A374040 A374040(n) = v374040[n];
%Y A374040 Cf. A003415, A007814, A007949, A085731.
%Y A374040 Some of the other matched sequences (see comments): A083345, A359430, A369001, A369004, A369643, A369658, A373143, A373474, A373483.
%Y A374040 Cf. also A322026, A353521, A369051, A373268, A372573, A374131 for similar and related constructions.
%Y A374040 Differs from A305900 first at n=77, where a(77) = 50, while A305900(77) = 59.
%K A374040 nonn
%O A374040 1,2
%A A374040 _Antti Karttunen_, Jul 01 2024