OFFSET
1,1
COMMENTS
tau(k) is the number of divisors of k (A000005).
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); ...
EXAMPLE
For n = 11; tau(2047) = tau(2049) = 4.
MATHEMATICA
Select[Range@ 200, Function[n, Equal @@ Map[DivisorSigma[0, 2^n + #] &, {-1, 1}]]] (* Michael De Vlieger, Mar 18 2017 *)
PROG
(Magma) [n: n in [1..500] | NumberOfDivisors(2^n - 1) eq NumberOfDivisors(2^n + 1)]
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 18 2017
STATUS
approved