A110174 - OEIS

A110174

Number of solutions 0<k<n to the equation phi(n) = phi(k) + phi(n-k), where phi is Euler's totient function.

0, 0, 2, 1, 0, 0, 0, 1, 2, 2, 0, 1, 0, 4, 4, 1, 0, 2, 0, 5, 4, 4, 0, 3, 4, 4, 4, 7, 0, 0, 0, 1, 6, 2, 2, 3, 0, 6, 2, 7, 0, 2, 0, 9, 6, 4, 0, 3, 0, 4, 6, 9, 0, 4, 2, 9, 4, 2, 0, 1, 0, 4, 4, 1, 4, 4, 0, 9, 4, 4, 0, 5, 0, 4, 8, 9, 2, 6, 0, 7, 0, 2, 0, 3, 4, 4, 8, 9, 0, 2, 0, 11, 8, 4, 0, 3, 0, 2, 6, 9, 0, 6, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

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

MATHEMATICA

a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; Table[Length[a[n]], {n, 150}]

PROG

(PARI) A110174(n) = { my(ph=eulerphi(n)); sum(k=1, n-1, (ph == (eulerphi(k)+eulerphi(n-k)))); }; \\ Antti Karttunen, Feb 20 2023

CROSSREFS

Cf. A110173 (least k such that phi(n) = phi(k) + phi(n-k)).

Cf. also A110177.