A179202 Numbers n such that phi(n) = phi(n+8), with Euler's totient function phi=A000010.

13, 16, 19, 25, 28, 32, 40, 70, 104, 128, 175, 182, 209, 280, 296, 488, 551, 584, 657, 715, 806, 910, 1232, 1256, 1544, 1602, 2022, 2048, 2216, 2288, 2504, 2540, 2590, 2717, 2912, 3176, 3368, 3640, 3656, 4060, 4328, 4904, 5246, 5288, 5320, 5384, 5864, 5969

Offset: 1

Author

M. F. Hasler, Jan 05 2011

Keywords

• nonn

Comments

Among the 5596 terms below 10^7, a(6)=32 is the only term such that a(n+1) = a(n)+8.

There are 141741552 terms under 10^12. - Jud McCranie, Feb 13 2012

If a(n) is even then a(n)/2 is in A179186 - see comment at A217139. - Jud McCranie, Dec 31 2012

Links

• M. F. Hasler and Jud McCranie, Table of n, a(n) for n = 1..10000 (first 5596 terms from M. F. Hasler)
• F. Firoozbakht, Puzzle 466. phi(n-1)=phi(n)=phi(n+1), in C. Rivera's Primepuzzles.
• Kevin Ford, Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k), arXiv:2002.12155 [math.NT], 2020.

Crossrefs

Cf. A000010, A001274, A001494, A179186, A179187, A179188, A179189, A007015.

Programs

Magma

[n: n in [1..10000] | EulerPhi(n) eq EulerPhi(n+8)]; // Vincenzo Librandi, Sep 08 2016

Mathematica

Select[Range[6000], EulerPhi[#] == EulerPhi[# + 8] &] (* Vincenzo Librandi, Sep 08 2016 *)

PARI

{op=vector(N=8); for( n=1, 1e4, if( op[n%N+1]+0==op[n%N+1]=eulerphi(n), print1(n-N, ", ")))}

Formula

A000010(a(n)) = A000010(a(n)+8).