A362042 Number of odd semiprimes less than 2^n.

0, 0, 0, 0, 2, 4, 11, 24, 51, 103, 207, 417, 815, 1622, 3164, 6210, 12146, 23711, 46295, 90307, 176369, 344155, 672091, 1312721, 2565048, 5013566, 9804910, 19183069, 37547164, 73526846, 144042323, 282317826, 553564500, 1085869406, 2130916524, 4183381508, 8215884036

Offset: 0

Author

Sidney Cadot, Apr 15 2023

Keywords

• nonn

Comments

Odd numbers with two prime factors are used as the modulus in the RSA algorithm. This sequence shows the growth of the number of 'candidate' RSA moduli for keys up to a given number of bits.

Examples

			For n=5, there are four integers less than 32 (i.e., 2^5) that are the product of two odd primes: {3*3, 3*5, 3*7, 5*5} = {9, 15, 21, 25}; hence, a(5)=4.
		

Crossrefs

Cf. A046315, A007053, A085770, A125527.

Programs

Mathematica

a[n_]:=Length@Select[Range[1, 2^n - 1, 2], Total[Last /@ FactorInteger[#]] == 2 &]
Table[a[n],{n,0,24}]

Formula

a(n) = A125527(n) - A007053(n-1) for n > 0. - Jinyuan Wang, Apr 16 2023

Extensions

More terms from Jinyuan Wang, Apr 16 2023