A179188 Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010.

24, 34, 36, 39, 43, 44, 57, 72, 78, 82, 84, 93, 96, 108, 111, 146, 178, 201, 216, 222, 225, 226, 228, 306, 327, 364, 366, 381, 399, 417, 432, 438, 442, 466, 471, 482, 516, 527, 540, 543, 562, 576, 597, 610, 626, 633, 648, 706, 714, 732, 738, 802, 818, 866, 898, 912, 921, 924, 942, 948, 972, 1011

Offset: 1

Author

M. F. Hasler, Jan 05 2011

Keywords

• nonn

Comments

There are 1385502728 terms under 10^12. - Jud McCranie, Feb 13 2012

Links

• Jud McCranie, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• 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, A007015.

Programs

Magma

[n: n in [1..1000] | EulerPhi(n) eq EulerPhi(n+6)]; // Vincenzo Librandi, Sep 08 2016

Mathematica

Flatten[Position[Partition[EulerPhi[Range[1200]],7,1],?(#[[1]] == #[[7]]&),{1},Heads->False]] (* _Harvey P. Dale, Jan 30 2016 *)
Select[Range[1000], EulerPhi[#] == EulerPhi[# + 6] &] (* Vincenzo Librandi, Sep 08 2016 *)

PARI

{op=vector(N=6); 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)+6).