cp's OEIS Frontend

A328767 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where for n>1, f(n) = [A003415(i), A328382(i)], and f(1) = 1.

%I A328767 #7 Oct 28 2019 20:00:53
%S A328767 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,14,17,18,19,2,
%T A328767 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,22,34,35,36,2,37,
%U A328767 38,39,40,41,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,46,55,2,56,57,58,2,59,60,61,62,63,2,64,65,66,67,68,69,70,2,71,72,73,2,74,2
%N A328767 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where for n>1, f(n) = [A003415(i), A328382(i)], and f(1) = 1.
%C A328767 For all i, j:
%C A328767   A305800(i) = A305800(j) => a(i) = a(j),
%C A328767   a(i) = a(j) => A327858(i) = A327858(j),
%C A328767   a(i) = a(j) => A328098(i) = A328098(j),
%H A328767 Antti Karttunen, <a href="/A328767/b328767.txt">Table of n, a(n) for n = 1..65537</a>
%o A328767 (PARI)
%o A328767 up_to = 65537;
%o A328767 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 A328767 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328767 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328767 A328382(n) = (A276086(n)%A003415(n));
%o A328767 Aux328767(n) = if(1==n,1,[A003415(n), A328382(n)]);
%o A328767 v328767 = rgs_transform(vector(up_to, n, Aux328767(n)));
%o A328767 A328767(n) = v328767[n];
%Y A328767 Cf. A003415, A305800, A327858, A328098, A328382.
%Y A328767 Cf. also A300245, A300249, A327970.
%K A328767 nonn
%O A328767 1,2
%A A328767 _Antti Karttunen_, Oct 28 2019