cp's OEIS Frontend

A216480 Primitive non-solvable numbers: orders of non-solvable groups such that all groups with order a proper divisor of that order are solvable.

%I A216480 #20 May 10 2018 03:31:32
%S A216480 60,168,504,1092,2448,5616,6072,9828,25308,28224,32736,39732,51888,
%T A216480 74412,150348,194472,285852,456288,546312,612468,721392,1024128,
%U A216480 1285608,1934868,2097024,2165292,2328648,2588772,3594432,3822588,5544672,5848428,6324552,7174332,8487168,9095592
%N A216480 Primitive non-solvable numbers: orders of non-solvable groups such that all groups with order a proper divisor of that order are solvable.
%C A216480 Primitive elements of A056866; consequently, each term is divisible by 4 and either 3 or 5.
%C A216480 That is, numbers n such that n is in A056866, but no smaller m dividing n is in A056866. - _Charles R Greathouse IV_, May 09 2018
%H A216480 Charles R Greathouse IV, <a href="/A216480/b216480.txt">Table of n, a(n) for n = 1..10000</a>
%F A216480 a(n) ~ kn^3 log^3 n, where k = 27/8. - _Charles R Greathouse IV_, Sep 11 2012
%o A216480 (PARI) list(lim)={
%o A216480     my(v=List([5616]),t);
%o A216480     forprime(p=2,log(lim)\log(8)+2,
%o A216480         listput(v,(4^p-1)<<p)
%o A216480     );
%o A216480     forprime(p=3,log(2*lim)\log(27)+2,
%o A216480         listput(v,3^p*(9^p\2))
%o A216480     );
%o A216480     forprime(p=3,log(lim)\log(32)+2,
%o A216480         listput(v,(4^p-1)*(2^p-1)<<(2*p))
%o A216480     );
%o A216480     forprime(p=7,sqrtn(2*lim,3)+1,
%o A216480         if(p%5>1 && p%5<4, listput(v,p^2\2*p))
%o A216480     );
%o A216480     vecsort(select(n->n<=lim,Vec(v)))
%o A216480 };
%Y A216480 Cf. A056866.
%K A216480 nonn,nice
%O A216480 1,1
%A A216480 _Charles R Greathouse IV_, Sep 11 2012