A276503 -id:A276503 - cp's OEIS frontend

A276504 Numbers n such that phi(n) = phi(n+11), with Euler's totient function phi = A000010.

7, 11, 27, 33, 45, 63, 135, 165, 285, 304, 345, 765, 855, 964, 1144, 1575, 1744, 2134, 2295, 2805, 6424, 6604, 10725, 23584, 24244, 27645, 28875, 31174, 31354, 35445, 40755, 44164, 46672, 57046, 57057, 61444, 64005, 78975, 82095, 90195

Offset: 1

Vincenzo Librandi, Sep 08 2016

Kevin Ford, Solutions of phi(n) = phi(n+k) and sigma(n) = sigma(n + k), arXiv:2002.12155 [math.NT], 2020.

Cf. A000010.

Cf. similar sequences listed in A276503.

[n: n in [1..100000] | EulerPhi(n) eq EulerPhi(n+11)];

Select[Range[150000], EulerPhi[#] == EulerPhi[# + 11] &]

A330251 Numbers k such that phi(k) = phi(k+3), where phi (A000010) is Euler's totient function.

Original entry on oeis.org

3, 5, 8720288051472, 9134280520365, 41544070492925, 42466684755492, 51363581614342, 68616494581632, 113312918293575, 210911076210835, 215517565688425, 294988451482725, 383617980270525, 432759876053505, 442863123838135, 532068058516992, 892813363927485, 923102743748185, 929531173876305

Offset: 1

Michel Marcus and Giovanni Resta, Feb 29 2020

nonn

10^15 < a(20) <= 1089641067389872.
Also terms: 1248817919303952, 1332436545865422, 1394926716616125, 1868522795664525, 1950445682260072.
a(4) and a(9) appear in Kevin Ford's paper.

Kevin Ford, Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k), arXiv:2002.12155 [math.NT], 2020.
S. W. Graham, J. J. Holt, and C. Pomerance, On the solutions to phi(n) = phi(n+k), Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867-882.
Mathematics StackExchange, Conjecture on the gap between integers having the same number of co-primes, Sep 25 2019.

Cf. A000010, A007015.
Cf. A001274, A001494, A179186, A179187, A179188, A179189, A179202, A330429.
Cf. A276503, A276504, A217139.

Select[Range[100000], EulerPhi[#] == EulerPhi[# + 3] &] (* Alonso del Arte, Mar 01 2020 *)

isok(k) = eulerphi(k) == eulerphi(k+3); \\ Michel Marcus, Feb 29 2020

A330429 Numbers k such that phi(k) = phi(k+9), where phi (A000010) is Euler's totient function.

Original entry on oeis.org

9, 15, 1005079920836, 13695542245376, 26160864154416, 27402841561095, 27599063056565, 110263115897935, 124632211478775, 127400054266476, 154090744843026, 205849483744896, 231019991767556, 339938754880725, 459718637643265, 632733228632505, 646552697065275, 683008674773416, 884965354448175

Offset: 1

Giovanni Resta, Mar 01 2020

nonn

a(20) > 10^15.

Kevin Ford, Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k), arXiv:2002.12155 [math.NT], 2020.
S. W. Graham, J. J. Holt, and C. Pomerance, On the solutions to phi(n) = phi(n+k), Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867-882.

Cf. A000010, A007015.
Cf. A001274, A001494, A330251, A179186, A179187, A179188, A179189, A179202.
Cf. A276503, A276504, A217139.

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A276504 Numbers n such that phi(n) = phi(n+11), with Euler's totient function phi = A000010.

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A330251 Numbers k such that phi(k) = phi(k+3), where phi (A000010) is Euler's totient function.

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A330429 Numbers k such that phi(k) = phi(k+9), where phi (A000010) is Euler's totient function.

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