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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Oct 28 2019

Keywords

• nonn

Comments

For all i, j:

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

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Cf. also A300245, A300249, A327970.

Programs

PARI

up_to = 65537;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328382(n) = (A276086(n)%A003415(n));
Aux328767(n) = if(1==n,1,[A003415(n), A328382(n)]);
v328767 = rgs_transform(vector(up_to, n, Aux328767(n)));
A328767(n) = v328767[n];