A276503 Numbers n such that phi(n) = phi(n+10), with Euler's totient function phi = A000010.

20, 26, 35, 100, 130, 160, 370, 400, 610, 730, 793, 1000, 1570, 1843, 1930, 2500, 2560, 2770, 2860, 3130, 3970, 4000, 4171, 4210, 4570, 5410, 5767, 6130, 6400, 6610, 6730, 7330, 7570, 8770, 9106, 9640, 9970, 9991, 10498, 10660, 10930, 11248

Offset: 1

Author

Vincenzo Librandi, Sep 08 2016

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1200
• Kevin Ford, Solutions of phi(n) = phi(n+k) and sigma(n) = sigma(n + k), arXiv:2002.12155 [math.NT], 2020.

Crossrefs

Cf. A000010.

Cf. numbers n such that phi(n)=phi(n+k): A001274 (k=1), A001494 (k=2), A179186 (k=4), A179187 (k=5), A179188 (k=6), A179189 (k=7), A179202 (k=8), this sequence (k=10), A276504 (k=11), A217139 (k=12).

Programs

Magma

[n: n in [1..20000] | EulerPhi(n) eq EulerPhi(n+10)];

Mathematica

Select[Range[15000], EulerPhi[#] == EulerPhi[# + 10] &]
SequencePosition[EulerPhi[Range[12000]],{x_,,,_,,,_,,,_,x_}][[;;,1]] (* Harvey P. Dale, Apr 29 2025 *)