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Odd numbers k such that k and k+2 both have at least two divisors with the same value of the Euler totient function (A000010).
2

%I #8 Jun 08 2024 15:45:05

%S 2107,11275,42651,68733,90153,99123,123633,213003,226825,242305,

%T 262143,272853,292873,295405,308007,313443,376675,376803,378693,

%U 390115,427425,471293,473263,524797,525481,556983,579535,591325,618469,638163,663325,669123,699853,731815

%N Odd numbers k such that k and k+2 both have at least two divisors with the same value of the Euler totient function (A000010).

%C Numbers k such that k and k+2 are both in A359563.

%H Amiram Eldar, <a href="/A373527/b373527.txt">Table of n, a(n) for n = 1..10000</a>

%t q[n_] := q[n] = UnsameQ @@ EulerPhi[Divisors[n]]; Select[Range[1, 10^6, 2], ! q[#] && ! q[# + 2] &]

%o (PARI) is(k) = k>1 && k%2 && numdiv(k) > #Set(apply(x->eulerphi(x), divisors(k)));

%o lista(kmax) = {my(q1 = 0, q2); forstep(k = 3, kmax, 2, q2 = is(k); if(q1 && q2, print1(k-2, ", ")); q1 = q2);}

%Y Subsequence of A359563.

%Y A373528 is a subsequence.

%Y Cf. A000010, A102190.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jun 08 2024