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A247174 Numbers k such that phi(k) = phi(k+1) and simultaneously Product_{d|k} phi(d) = Product_{d|(k+1)} phi(d) where phi(x) = Euler totient function (A000010).

%I A247174 #20 Jul 17 2022 02:21:34
%S A247174 1,3,15,255,65535,2200694,2619705,6372794,40588485,76466985,81591194,
%T A247174 118018094,206569605,470542485,525644385,726638834,791937614,
%U A247174 971122514,991172805
%N A247174 Numbers k such that phi(k) = phi(k+1) and simultaneously Product_{d|k} phi(d) = Product_{d|(k+1)} phi(d) where phi(x) = Euler totient function (A000010).
%C A247174 Numbers n such that A000010(n) = A000010(n+1) and simultaneously A029940(n) = A029940(n+1).
%C A247174 4294967295 is also a term of this sequence.
%C A247174 Intersection of A001274 and A248795.
%H A247174 Amiram Eldar, <a href="/A247174/b247174.txt">Table of n, a(n) for n = 1..213</a> (terms below 10^13, calculated using the b-file at A001274)
%e A247174 15 is in the sequence because phi(15) = phi(16) = 8 and simultaneously Product_{d|15} phi(d) = Product_{d|(15+1)} phi(d) = 64.
%t A247174 a247174[n_Integer] := Module[{a001274, a248795},
%t A247174   a001274[m_] := Select[Range[m], EulerPhi[#] == EulerPhi[# + 1] &];
%t A247174   a248795[m_] :=
%t A247174    Select[Range[m],
%t A247174     Product[EulerPhi[i], {i, Divisors[#]}] ==
%t A247174       Product[EulerPhi[j], {j, Divisors[# + 1]}] &];
%t A247174 Intersection[a001274[n], a248795[n]]] (* _Michael De Vlieger_, Dec 01 2014 *)
%o A247174 (Magma) [n: n in [1..100000] |  (&*[EulerPhi(d): d in Divisors(n)]) eq (&*[EulerPhi(d): d in Divisors(n+1)]) and EulerPhi(n) eq EulerPhi(n+1)]
%o A247174 (Magma) [n: n in [A248795(n)] | EulerPhi(n) eq EulerPhi(n+1)]
%Y A247174 Cf. A000010, A001274, A029940, A248795.
%K A247174 nonn
%O A247174 1,2
%A A247174 _Jaroslav Krizek_, Nov 22 2014
%E A247174 a(6)-a(19) using A248795 by _Jaroslav Krizek_, Nov 25 2014