cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7
Offset: 1

Views

Author

Lucas A. Brown, Oct 13 2022

Keywords

Comments

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

Crossrefs

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).

A357741 Semiprimes k such that k is divisible by its index in the sequence of semiprimes.

Original entry on oeis.org

4, 6, 9, 21, 33, 129, 159, 3066835, 3067195, 3067255, 3067615, 3067745, 3068045, 44690978227, 44690978647, 44690978983, 44690979529
Offset: 1

Views

Author

Lucas A. Brown, Oct 13 2022

Keywords

Comments

No further terms <= 8040423200947. - Lucas A. Brown, Oct 13 2022
Conjecture: a(18) > 10^17. - Martin Ehrenstein, Oct 28 2022

Examples

			The 1st semiprime is 4, which is divisible by 1, so 4 is in the sequence.
The 4th semiprime is 10, which is not divisible by 4, so 10 is not in the sequence.
The 7th semiprime is 21, which is divisible by 7, so 21 is in the sequence.
		

Crossrefs

Formula

a(n) = A001358(A106125(n))
Showing 1-2 of 2 results.