A356764 Semiprimes divisible by their indices in the sequence of semiprimes, divided by those indices.

4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7

Offset: 1

Author

Lucas A. Brown, Oct 13 2022

Keywords

• nonn
• hard
• more

Comments

Except for a(1) = 4, all terms are prime.

Links

• Lucas A. Brown, semiprimemods.py

Crossrefs

Cf. A001358, A106125, A357741.

Programs

Mathematica

With[{sp=Select[Range[5*10^6],PrimeOmega[#]==2&]},Select[#[[1]]/#[[2]]&/@Thread[{sp,Range[Length[sp]]}],IntegerQ]] (* The program generates the first 13 terms of the sequence. *) (* Harvey P. Dale, Aug 07 2025 *)

Formula

a(n) = A357741(n) / A106125(n).