A179189 Numbers n such that phi(n) = phi(n+7), with Euler's totient function phi = A000010.

5, 7, 21, 45, 75, 105, 285, 488, 585, 765, 1148, 1275, 1358, 1785, 2528, 3465, 4088, 6825, 9405, 12375, 14348, 15345, 16208, 16988, 23648, 25905, 25935, 42698, 50018, 52845, 54615, 61448, 62865, 68445, 78195, 80025, 82005, 88328, 93555, 98475

Offset: 1

Author

M. F. Hasler, Jan 05 2011

Keywords

• nonn

Comments

There are 40 terms below 10^5, 81 terms below 10^6 and 162 terms below 10^7. There are 6606 terms below 10^12. [Jud McCranie, Feb 13 2012]

Farideh Firoozbakht asks whether there is some a(n+1) = a(n)+7, cf. link.

For n < 10^13, the only n such that phi(n-7) = phi(n) = phi(n+7) is 30057431145. - Giovanni Resta, Feb 27 2014

Links

• Jud McCranie, Table of n, a(n) for n = 1..6606 (terms < 10^12)
• 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, A007015.

Programs

Magma

[n: n in [1..100000] | EulerPhi(n) eq EulerPhi(n+7)]; // Vincenzo Librandi, Sep 08 2016

Mathematica

Select[Range[100000], EulerPhi[#] == EulerPhi[# + 7] &] (* Vincenzo Librandi, Sep 08 2016 *)

PARI

{op=vector(N=7); for( n=1, 1e5, if( op[n%N+1]+0==op[n%N+1]=eulerphi(n), print1(n-N, ", ")))}

Formula

A000010(a(n)) = A000010(a(n)+7).