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

60, 168, 504, 1092, 2448, 5616, 6072, 9828, 25308, 28224, 32736, 39732, 51888, 74412, 150348, 194472, 285852, 456288, 546312, 612468, 721392, 1024128, 1285608, 1934868, 2097024, 2165292, 2328648, 2588772, 3594432, 3822588, 5544672, 5848428, 6324552, 7174332, 8487168, 9095592

Offset: 1

Author

Charles R Greathouse IV, Sep 11 2012

Keywords

• nonn
• nice

Comments

Primitive elements of A056866; consequently, each term is divisible by 4 and either 3 or 5.

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

Links

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

Crossrefs

Cf. A056866.

Programs

PARI

list(lim)={
    my(v=List([5616]),t);
    forprime(p=2,log(lim)\log(8)+2,
        listput(v,(4^p-1)<1 && p%5<4, listput(v,p^2\2*p))
    );
    vecsort(select(n->n<=lim,Vec(v)))
};

Formula

a(n) ~ kn^3 log^3 n, where k = 27/8. - Charles R Greathouse IV, Sep 11 2012