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A216480 Primitive non-solvable numbers: orders of non-solvable groups such that all groups with order a proper divisor of that order are solvable. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 06:05 EDT 2020. Contains 337166 sequences. (Running on oeis4.)