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

1,1

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

Formula

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

Prog

(PARI) list(lim)={
    my(v=List([5616]), t);
    forprime(p=2, log(lim)\log(8)+2,
        listput(v, (4^p-1)<<p)
    );
    forprime(p=3, log(2*lim)\log(27)+2,
        listput(v, 3^p*(9^p\2))
    );
    forprime(p=3, log(lim)\log(32)+2,
        listput(v, (4^p-1)*(2^p-1)<<(2*p))
    );
    forprime(p=7, sqrtn(2*lim, 3)+1,
        if(p%5>1 && p%5<4, listput(v, p^2\2*p))
    );
    vecsort(select(n->n<=lim, Vec(v)))
};

Crossrefs

Cf. A056866.

Sequence in context: A330584 A330586 A119630 * A257146 A291549 A259946

Adjacent sequences: A216477 A216478 A216479 * A216481 A216482 A216483

Keyword

nonn,nice

Author

Charles R Greathouse IV, Sep 11 2012

Status

approved