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.

A075730 Squares of odd semiprimes A046315, odd numbers divisible by exactly 2 primes (counted with multiplicity).

Original entry on oeis.org

81, 225, 441, 625, 1089, 1225, 1521, 2401, 2601, 3025, 3249, 4225, 4761, 5929, 7225, 7569, 8281, 8649, 9025, 12321, 13225, 14161, 14641, 15129, 16641, 17689, 19881, 20449, 21025, 24025, 25281, 25921, 28561, 31329, 33489, 34225, 34969, 40401
Offset: 1

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Author

Jani Melik, Oct 07 2002

Keywords

Examples

			9 is odd and divisible by 3 (twice) and 9*9=81.
15 is odd and divisible by 3 and 5 and 15*15=225.
		

Crossrefs

Equals A046315(n)^2.

Programs

  • Maple
    readlib(issqr): ts_kv_sp_lih := proc(n); if (numtheory[bigomega](n)=4 and type(n,odd)='true' and issqr(n)='true') then RETURN(n); fi; end: seq(ts_kv_sp_lih(i), i=1..100000);
  • Mathematica
    Select[Range[1, 201, 2], PrimeOmega[#] == 2 &]^2 (* Amiram Eldar, Mar 22 2021 *)

Formula

Sum_{n>=1} 1/a(n) = P(2)^2/2 + P(4)/2 - P(2)/4 = 0.02769857933..., where P is the prime zeta function. - Amiram Eldar, Mar 22 2021

Extensions

Checked by Zak Seidov, Mar 08 2006