A247174 Numbers k such that phi(k) = phi(k+1) and simultaneously Product_{d|k} phi(d) = Product_{d|(k+1)} phi(d) where phi(x) = Euler totient function (A000010).

1, 3, 15, 255, 65535, 2200694, 2619705, 6372794, 40588485, 76466985, 81591194, 118018094, 206569605, 470542485, 525644385, 726638834, 791937614, 971122514, 991172805

Offset: 1

Author

Jaroslav Krizek, Nov 22 2014

Keywords

• nonn

Comments

Numbers n such that A000010(n) = A000010(n+1) and simultaneously A029940(n) = A029940(n+1).

4294967295 is also a term of this sequence.

Intersection of A001274 and A248795.

Examples

			15 is in the sequence because phi(15) = phi(16) = 8 and simultaneously Product_{d|15} phi(d) = Product_{d|(15+1)} phi(d) = 64.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..213 (terms below 10^13, calculated using the b-file at A001274)

Crossrefs

Cf. A000010, A001274, A029940, A248795.

Programs

Magma

[n: n in [1..100000] |  (&*[EulerPhi(d): d in Divisors(n)]) eq (&*[EulerPhi(d): d in Divisors(n+1)]) and EulerPhi(n) eq EulerPhi(n+1)]

Magma

[n: n in [A248795(n)] | EulerPhi(n) eq EulerPhi(n+1)]

Mathematica

a247174[n_Integer] := Module[{a001274, a248795},
  a001274[m_] := Select[Range[m], EulerPhi[#] == EulerPhi[# + 1] &];
  a248795[m_] :=
   Select[Range[m],
    Product[EulerPhi[i], {i, Divisors[#]}] ==
      Product[EulerPhi[j], {j, Divisors[# + 1]}] &];
Intersection[a001274[n], a248795[n]]] (* Michael De Vlieger, Dec 01 2014 *)

Extensions

a(6)-a(19) using A248795 by Jaroslav Krizek, Nov 25 2014