A110173 Least k such that phi(n) = phi(k) + phi(n-k) for 0

0, 0, 1, 2, 0, 0, 0, 4, 4, 4, 0, 6, 0, 4, 5, 8, 0, 6, 0, 6, 5, 6, 0, 6, 6, 4, 11, 6, 0, 0, 0, 16, 6, 8, 10, 12, 0, 4, 13, 12, 0, 12, 0, 6, 7, 8, 0, 12, 0, 10, 16, 6, 0, 6, 26, 12, 19, 26, 0, 30, 0, 4, 12, 32, 24, 24, 0, 6, 23, 28, 0, 18, 0, 10, 12, 8, 24, 12, 0, 24, 0, 8, 0, 24, 8, 4, 6, 12, 0, 30

Offset: 1

Author

T. D. Noe, Jul 15 2005

Keywords

• nonn

Comments

Sequence A110174 gives the number of solutions 0A110175.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A066426 (least k such that phi(n)+phi(k)=phi(n+k)), A110174.

Cf. also A110176.

Programs

Mathematica

a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; Table[s=a[n]; If[Length[s]==0, 0, First[s]], {n, 150}]

PARI

A110173(n) = { my(ph=eulerphi(n)); for(k=1,n-1,if(ph == (eulerphi(k)+eulerphi(n-k)), return(k))); (0); }; \\ Antti Karttunen, Feb 20 2023