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

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.

Sequence in context: A340655 A035172 A344858 * A022909 A292136 A032239

Adjacent sequences: A110171 A110172 A110173 * A110175 A110176 A110177

Keyword

nonn,look

Author

T. D. Noe, Jul 15 2005

Status

approved