A283930 Numbers k such that tau(2^k - 1) = tau(2^k + 1).

2, 11, 14, 21, 23, 29, 45, 47, 53, 71, 73, 74, 82, 86, 95, 99, 101, 105, 113, 115, 121, 142, 167, 169, 179, 181, 199, 203, 209, 233, 235, 277, 307, 311, 317, 335, 337, 343, 347, 349, 353, 355, 358, 361, 382, 434, 449, 465, 494, 509, 515, 518, 529, 535, 547, 549, 570, 583, 585, 599

Offset: 1

Author

Jaroslav Krizek, Mar 18 2017

Keywords

• nonn

Comments

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

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

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

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, ...

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

Examples

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

Crossrefs

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

Programs

Magma

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

Mathematica

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

PARI

for(n=1, 600, if(numdiv(2^n - 1) == numdiv(2^n + 1), print1(n,", "))) \\ Indranil Ghosh, Mar 18 2017

Python

from sympy import divisor_count
print([n for n in range(1, 601) if divisor_count(2**n + 1) == divisor_count(2**n - 1)]) # Indranil Ghosh, Mar 18 2017