A110173 Least k such that phi(n) = phi(k) + phi(n-k) for 0<k<n, or 0 if there is no such k, where phi is Euler's totient function.

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

1,4

Comments

Sequence A110174 gives the number of solutions 0<k<n. Note that a(n)=0 for all primes except 3. It is also zero for the composite numbers in A110175.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

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}]

Prog

(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

Crossrefs

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

Cf. also A110176.

Sequence in context: A280292 A181566 A348513 * A328820 A259863 A283666

Adjacent sequences: A110170 A110171 A110172 * A110174 A110175 A110176

Keyword

nonn

Author

T. D. Noe, Jul 15 2005

Status

approved