A266267 Numbers n such that phi(n) = k*phi(n-k) for some number 1 <= k < n - 2.

4, 5, 7, 8, 9, 11, 13, 16, 17, 32, 73, 105, 165, 195, 256, 257, 496, 512, 527, 585, 976, 992, 1952, 2205, 2522, 2593, 2626, 2835, 3256, 3706, 5187, 5188, 5252, 6512, 7412, 10013, 10376, 10605, 11716, 13366, 13653, 18316, 21423, 22936, 23103, 23432, 23717

Offset

1,1

Comments

Prime terms are in A266266.

For all primes p we have: phi(p) = k*phi(p-k) if k = p - 1.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..102

Example

17 is in the sequence because phi(17) = 16 = 2*phi(15) = 2*8.

Mathematica

Select[Range@ 1000, Function[n, AnyTrue[Range[n - 2], EulerPhi@ n == # EulerPhi[n - #] &]]] (* Michael De Vlieger, Jan 09 2016, Version 10 *)
f[n_] := f[n] = EulerPhi@ n; k = 1; lst = {}; fQ[n_] := Block[{k = 1, ep = f@ n}, While[k + 2 < n && ep != k*f[n - k], k++]; k + 2 < n]; Select[ Range@ 25000, fQ@# &] (* Robert G. Wilson v, Jan 23 2016 *)

Prog

(Magma) Set(Sort([4, 5] cat [n: n in [6..100000], k in [1..5] | EulerPhi(n) eq k*EulerPhi(n-k)]))
(PARI) isok(n) = for (k=1, n-2, if (eulerphi(n) == k*eulerphi(n-k), return(1))); \\ Michel Marcus, Dec 27 2015

Crossrefs

Cf. A000010, A019434, A266266.

Sequence in context: A164515 A298871 A298874 * A189477 A047494 A080712

Adjacent sequences: A266264 A266265 A266266 * A266268 A266269 A266270

Keyword

nonn

Author

Jaroslav Krizek, Dec 26 2015

Status

approved