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

0,5

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.

Links

Table of n, a(n) for n=0..36.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A046315, A007053, A085770, A125527.

Sequence in context: A103669 A230711 A034485 * A018006 A183510 A230984

Adjacent sequences: A362039 A362040 A362041 * A362043 A362044 A362045

Keyword

nonn

Author

Sidney Cadot, Apr 15 2023

Extensions

More terms from Jinyuan Wang, Apr 16 2023

Status

approved