A322874 Ordinal transform of A007431, which is Möbius transform of Euler phi.

1, 1, 2, 3, 1, 2, 1, 1, 1, 3, 1, 4, 1, 4, 2, 2, 1, 5, 1, 3, 2, 6, 1, 2, 1, 7, 1, 3, 1, 8, 1, 1, 2, 9, 2, 3, 1, 10, 2, 1, 1, 11, 1, 3, 2, 12, 1, 4, 1, 13, 3, 3, 1, 14, 2, 1, 2, 15, 1, 4, 1, 16, 1, 2, 1, 17, 1, 4, 2, 18, 1, 2, 1, 19, 3, 3, 2, 20, 1, 3, 2, 21, 1, 4, 3, 22, 3, 1, 1, 23, 1, 3, 2, 24, 2, 3, 1, 25, 3, 4, 1, 26, 1, 1, 5

Offset: 1

Author

Antti Karttunen, Dec 29 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A007431, A081373, A303756, A322873.

Programs

Mathematica

A007431[n_] := Sum[EulerPhi[d] MoebiusMu[n/d], {d, Divisors[n]}];
b[_] = 0;
a[n_] := a[n] = With[{t = A007431[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 20 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; };
A007431(n) = sumdiv(n,d,moebius(n/d)*eulerphi(d));
v322874 = ordinal_transform(vector(up_to,n,A007431(n)));
A322874(n) = v322874[n];