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%I #11 Sep 02 2016 15:23:20
%S 15,21,33,35,39,51,55,57,65,69,77,85,91,95,115,119,133,143,145,155,
%T 161,187,203,209,217,221,247,253,259,299,319,323,341,377,391,403,407,
%U 437,451,473,481,493,517,527,533,551,559,583,589,611,629,667
%N Semiprimes pq such that p, q are odd primes and p < q <= 4p+11.
%C 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."
%H Charles R Greathouse IV, <a href="/A128907/b128907.txt">Table of n, a(n) for n = 1..10000</a>
%H Siu-Hung Ng, <a href="http://arXiv.org/abs/0704.2428">Hopf algebras of dimension pq, II</a>
%F {p*q such that p, q are odd primes and p < q <= 4*p+11}.
%t 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 *)
%o (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
%Y Cf. A000040, A001358, A046388.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 21 2007
%E Terms corrected by _Charles R Greathouse IV_, Dec 30 2013
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