1,1

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."

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Siu-Hung Ng, Hopf algebras of dimension pq, II

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

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

Cf. A000040, A001358, A046388.

Sequence in context: A046388 A056913 A002557 * A321644 A225709 A020162

Adjacent sequences: A128904 A128905 A128906 * A128908 A128909 A128910

easy,nonn

Jonathan Vos Post, Apr 21 2007

Terms corrected by Charles R Greathouse IV, Dec 30 2013

approved