A283930 - OEIS

%I #26 Sep 08 2022 08:46:19

%S 2,11,14,21,23,29,45,47,53,71,73,74,82,86,95,99,101,105,113,115,121,

%T 142,167,169,179,181,199,203,209,233,235,277,307,311,317,335,337,343,

%U 347,349,353,355,358,361,382,434,449,465,494,509,515,518,529,535,547,549,570,583,585,599

%N Numbers k such that tau(2^k - 1) = tau(2^k + 1).

%C tau(k) is the number of divisors of k (A000005).

%C Numbers k such that A046801(k) = A046798(k).

%C Numbers k such that A000005(A000225(k)) = A000005(A000051(k)).

%C Corresponding values of tau(2^k +- 1): 2, 4, 8, 12, 4, 8, 64, 8, 8, 8, 8, 32, 32, 32, 32, 256, 4, 1536, ...

%C Corresponding pairs of numbers (2^k - 1, 2^k + 1): (3, 5); (2047, 2049); (16383, 16385); (2097151, 2097153); (8388607, 8388609); ...

%e For n = 11; tau(2047) = tau(2049) = 4.

%t Select[Range@ 200, Function[n, Equal @@ Map[DivisorSigma[0, 2^n + #] &, {-1, 1}]]] (* _Michael De Vlieger_, Mar 18 2017 *)

%o (Magma) [n: n in [1..500] | NumberOfDivisors(2^n - 1) eq NumberOfDivisors(2^n + 1)]

%o (PARI) for(n=1, 600, if(numdiv(2^n - 1) == numdiv(2^n + 1), print1(n,", "))) \\ _Indranil Ghosh_, Mar 18 2017

%o (Python)

%o from sympy import divisor_count

%o print([n for n in range(1, 601) if divisor_count(2**n + 1) == divisor_count(2**n - 1)]) # _Indranil Ghosh_, Mar 18 2017

%Y Cf. A000005, A000051, A000225, A046798, A046801, A283931.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Mar 18 2017