A328767 - OEIS

%I #7 Oct 28 2019 20:00:53

%S 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 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 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 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 For all i, j:

%C   A305800(i) = A305800(j) => a(i) = a(j),

%C   a(i) = a(j) => A327858(i) = A327858(j),

%C   a(i) = a(j) => A328098(i) = A328098(j),

%H Antti Karttunen, <a href="/A328767/b328767.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A328382(n) = (A276086(n)%A003415(n));

%o Aux328767(n) = if(1==n,1,[A003415(n), A328382(n)]);

%o v328767 = rgs_transform(vector(up_to, n, Aux328767(n)));

%o A328767(n) = v328767[n];

%Y Cf. A003415, A305800, A327858, A328098, A328382.

%Y Cf. also A300245, A300249, A327970.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 28 2019