A128907 Semiprimes pq such that p, q are odd primes and p < q <= 4p+11.

15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 91, 95, 115, 119, 133, 143, 145, 155, 161, 187, 203, 209, 217, 221, 247, 253, 259, 299, 319, 323, 341, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 533, 551, 559, 583, 589, 611, 629, 667

Offset: 1

Author

Jonathan Vos Post, Apr 21 2007

Keywords

• easy
• nonn

Comments

These semiprimes, a subset of A046388, appear in Ng. Abstract: "Let H be a Hopf algebra of dimension pq over an algebraically closed field of characteristic zero, where p, q are odd primes with p < q < 4p+12. We prove that H is semisimple and thus isomorphic to a group algebra, or the dual of a group algebra."

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Siu-Hung Ng, Hopf algebras of dimension pq, II

Crossrefs

Cf. A000040, A001358, A046388.

Programs

Mathematica

pqopQ[n_]:=Module[{f=FactorInteger[n],f1},f1=f[[All,1]];Length[f1]== 2 && Min[f1]>2&&Max[f[[All,2]]]==1&&f1[[2]]<=4f1[[1]]+11]; Select[ Range[ 700], pqopQ] (* Harvey P. Dale, Sep 02 2016 *)

PARI

is(n)=my(f=factor(n)); #f~==2 && f[1,2]==1 && f[2,2]==1 && f[1,1]>2 && f[2,1] <= 4*f[1,1]+11 \\ Charles R Greathouse IV, Dec 30 2013

Formula

{p*q such that p, q are odd primes and p < q <= 4*p+11}.

Extensions

Terms corrected by Charles R Greathouse IV, Dec 30 2013