A309942 Numbers k such that 2^k - 1 and 2^k + 1 have the same number of prime factors, counted with multiplicity.
2, 10, 11, 14, 21, 23, 29, 39, 47, 50, 53, 55, 63, 71, 73, 74, 75, 82, 86, 95, 101, 105, 113, 115, 121, 142, 147, 150, 167, 169, 179, 181, 182, 190, 199, 203, 209, 233, 235, 253, 277, 285, 303, 307, 311, 317, 335, 337, 339, 342, 343, 347, 349, 353, 355, 358
Offset: 1
Keywords
Examples
a(1) = 2: 2^2 - 1 = 3 and 2^2 + 1 are both prime, a(2) = 10: 2^10 - 1 = 1023 = 3 * 11 * 31 and 2^10 + 1 = 1025 = 5^2 * 41 both have 3 prime factors.
Programs
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Magma
[m:m in [2..400]| &+[p[2]: p in Factorization(2^m-1)] eq &+[p[2]: p in Factorization(2^m+1)]]; // Marius A. Burtea, Aug 24 2019
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Mathematica
Select[Range[200], PrimeOmega[2^# - 1 ] == PrimeOmega[2^# + 1 ] &] (* Amiram Eldar, Aug 24 2019 *)
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PARI
for(k=1, 209, my(f=bigomega(2^k-1),g=bigomega(2^k+1));if(f==g,print1(k,", ")))
Extensions
More terms from Amiram Eldar, Aug 24 2019