A322872 Ordinal transform of A171462, where A171462(n) = n - A052126(n).

1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 2, 3, 3, 1, 4, 1, 2, 2, 1, 1, 3, 2, 1, 3, 2, 1, 3, 1, 4, 2, 1, 3, 4, 1, 2, 3, 2, 1, 4, 1, 2, 5, 1, 1, 3, 2, 3, 1, 2, 1, 6, 1, 3, 1, 1, 1, 4, 1, 2, 2, 4, 3, 4, 1, 1, 2, 5, 1, 5, 1, 2, 6, 3, 2, 4, 1, 2, 3, 1, 1, 5, 2, 1, 2, 3, 1, 6, 3, 2, 1, 1, 2, 3, 1, 4, 3, 4, 1, 2, 1, 3, 4

Offset: 1

Author

Antti Karttunen, Dec 29 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A052126, A171462, A081373, A303756, A322871.

Programs

Mathematica

A171462[n_] := If[n == 1, 0, Module[{f = FactorInteger[n], p},
     p = f[[-1, 1]]; n(p-1)/p]];
b[_] = 0;
a[n_] := a[n] = With[{t = A171462[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 21 2021 *)

PARI

up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A171462(n) = if(1==n,0,(n-(n/vecmax(factor(n)[, 1]))));
v322872 = ordinal_transform(vector(up_to,n,A171462(n)));
A322872(n) = v322872[n];