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A046100 Biquadratefree numbers. 13
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Differs from A023809 at entries 0, 81, 162, 225, 226, etc. - R. J. Mathar, Oct 18 2008

Density is 1/zeta(4) = A215267 = 0.923938.... - Charles R Greathouse IV, Sep 02 2015

A051903(a(n)) < 4. - Reinhard Zumkeller, Sep 03 2015

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Biquadratefree

MAPLE

A046100 := proc(n)

    option remember;

    local a, p, is4free;

    if n = 1 then

        return 1;

    else

        for a from procname(n-1)+1 do

            is4free := true ;

            for p in ifactors(a)[2] do

                if op(2, p) >= 4 then

                    is4free := false;

                    break;

                end if;

            end do:

            if is4free then

                return a;

            end if;

        end do:

    end if;

end proc: # R. J. Mathar, Aug 08 2012

MATHEMATICA

lst={}; Do[a=0; Do[If[FactorInteger[m][[n, 2]]>4, a=1], {n, Length[FactorInteger[m]]}]; If[a!=1, AppendTo[lst, m]], {m, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)

PROG

(PARI) is(n)=n==1 || vecmax(factor(n)[, 2])<4 \\ Charles R Greathouse IV, Jun 16 2012

(Sage)

def is_biquadratefree(n):

    for c in list(n.factor()) :

        if c[1] >= 4 : return false

    return true

def A046100_list(n) : return [i for i in (1..n) if is_biquadratefree(i)]

A046100_list(76) # Peter Luschny, Aug 08 2012

(Haskell)

a046100 n = a046100_list !! (n-1)

a046100_list = filter ((< 4) . a051903) [1..]

-- Reinhard Zumkeller, Sep 03 2015

CROSSREFS

Cf. A046101, A005117 (2-free), A004709 (3-free).

Cf. A051903, subsequence of A209061.

Sequence in context: A178210 A013938 A023809 * A023757 A115105 A121176

Adjacent sequences:  A046097 A046098 A046099 * A046101 A046102 A046103

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 6 14:47 EST 2019. Contains 329806 sequences. (Running on oeis4.)