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A179188 Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010. 14

%I

%S 24,34,36,39,43,44,57,72,78,82,84,93,96,108,111,146,178,201,216,222,

%T 225,226,228,306,327,364,366,381,399,417,432,438,442,466,471,482,516,

%U 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

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

%C There are 1385502728 terms under 10^12. - _Jud McCranie_, Feb 13 2012

%H T. D. Noe and Jud McCranie, <a href="/A179188/b179188.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%H F. Firoozbakht, <a href="http://www.primepuzzles.net/puzzles/puzz_466.htm">Puzzle 466. phi(n-1)=phi(n)=phi(n+1)</a>, in C. Rivera's Primepuzzles.

%H Kevin Ford, <a href="https://arxiv.org/abs/2002.12155">Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k)</a>, arXiv:2002.12155 [math.NT], 2020.

%F A000010(a(n)) = A000010(a(n)+6).

%t Flatten[Position[Partition[EulerPhi[Range[1200]],7,1],_?(#[[1]] == #[[7]]&),{1},Heads->False]] (* _Harvey P. Dale_, Jan 30 2016 *)

%t Select[Range[1000], EulerPhi[#] == EulerPhi[# + 6] &] (* _Vincenzo Librandi_, Sep 08 2016 *)

%o (PARI) {op=vector(N=6); for( n=1,1e4,if( op[n%N+1]+0==op[n%N+1]=eulerphi(n),print1(n-N,",")))}

%o (MAGMA) [n: n in [1..1000] | EulerPhi(n) eq EulerPhi(n+6)]; // _Vincenzo Librandi_, Sep 08 2016

%Y Cf. A000010, A001274, A001494, A179186, A179187, A007015.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jan 05 2011

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)