A362042 -id:A362042 - cp's OEIS frontend

A362318 Number of odd semiprimes between 2^(n-1) and 2^n.

0, 0, 0, 0, 2, 2, 7, 13, 27, 52, 104, 210, 398, 807, 1542, 3046, 5936, 11565, 22584, 44012, 86062, 167786, 327936, 640630, 1252327, 2448518, 4791344, 9378159, 18364095, 35979682, 70515477, 138275503, 271246674, 532304906, 1045047118, 2052464984, 4032502528

Offset: 0

Sidney Cadot, Apr 16 2023

nonn

This is the number of odd integers with precisely n bits that are the product of two (possibly identical) prime factors.

Odd numbers with two prime factors are used as the modulus in the RSA algorithm. This sequence gives the number of "candidate" RSA moduli having precisely n bits. Note that many of these candidates would not be suitable for cryptographic applications because they are easily factored.

Chai Wah Wu, Table of n, a(n) for n = 0..63 (using data in A120033 and A036378)

Cf. A036378, A046315, A120033, A362042.

a[n_] := Length@Select[Range[2^(n - 1) + 1, 2^n - 1, 2], Total[Last /@ FactorInteger[#]] ==2 &]Table[a[n],{n,0,25}]

a(n) = A362042(n) - A362042(n-1) for n>=1.

a(n) = A120033(n-1) - A036378(n-2) for n > 1. - Chai Wah Wu, Apr 24 2023

More terms from Chai Wah Wu, Apr 24 2023 (using data in A120033 and A036378)

cp's OEIS Frontend

A362318 Number of odd semiprimes between 2^(n-1) and 2^n.

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