cp's OEIS Frontend

A179202 Numbers n such that phi(n) = phi(n+8), with Euler's totient function phi=A000010.

%I A179202 #38 Sep 08 2022 08:45:54
%S A179202 13,16,19,25,28,32,40,70,104,128,175,182,209,280,296,488,551,584,657,
%T A179202 715,806,910,1232,1256,1544,1602,2022,2048,2216,2288,2504,2540,2590,
%U A179202 2717,2912,3176,3368,3640,3656,4060,4328,4904,5246,5288,5320,5384,5864,5969
%N A179202 Numbers n such that phi(n) = phi(n+8), with Euler's totient function phi=A000010.
%C A179202 Among the 5596 terms below 10^7, a(6)=32 is the only term such that a(n+1) = a(n)+8.
%C A179202 There are 141741552 terms under 10^12. - _Jud McCranie_, Feb 13 2012
%C A179202 If a(n) is even then a(n)/2 is in A179186 - see comment at A217139. - _Jud McCranie_, Dec 31 2012
%H A179202 M. F. Hasler and Jud McCranie, <a href="/A179202/b179202.txt">Table of n, a(n) for n = 1..10000</a> (first 5596 terms from M. F. Hasler)
%H A179202 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 A179202 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 A179202 A000010(a(n)) = A000010(a(n)+8).
%t A179202 Select[Range[6000], EulerPhi[#] == EulerPhi[# + 8] &] (* _Vincenzo Librandi_, Sep 08 2016 *)
%o A179202 (PARI) {op=vector(N=8); for( n=1, 1e4, if( op[n%N+1]+0==op[n%N+1]=eulerphi(n), print1(n-N, ", ")))}
%o A179202 (Magma) [n: n in [1..10000] | EulerPhi(n) eq EulerPhi(n+8)]; // _Vincenzo Librandi_, Sep 08 2016
%Y A179202 Cf. A000010, A001274, A001494, A179186, A179187, A179188, A179189, A007015.
%K A179202 nonn
%O A179202 1,1
%A A179202 _M. F. Hasler_, Jan 05 2011