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A230902 Positive numbers such that half of the set of divisors are of the form x^2 + x*y + y^2 (A003136) and half not (A034020). 0
2, 5, 6, 8, 11, 14, 15, 17, 18, 23, 24, 26, 29, 32, 33, 35, 38, 41, 42, 45, 47, 51, 53, 54, 56, 59, 62, 65, 69, 71, 72, 74, 77, 78, 83, 86, 87, 89, 95, 96, 98, 99, 101, 104, 105, 107, 113, 114, 119, 122, 123, 125, 126, 128, 131, 134, 135, 137, 141, 143, 146, 149, 152, 153, 155, 158, 159, 161, 162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

Triangle read by rows in which row n lists the divisors of n begins:

1(0^2+0*1+1^2);

1(0^2+0*1+1^2), 2;

1(0^2+0*1+1^2), 3(1^1+1*1+1^2);

1(0^2+0*1+1^2), 2, 4(0^2+0*2+2^2);

1(0^2+0*1+1^2), 5;

1(0^2+0*1+1^2), 2, 3(1^1+1*1+1^2), 6;

1(0^2+0*1+1^2), 7(1^1+1*2+2^2);

1(0^2+0*1+1^2), 2, 4(0^2+0*2+2^2), 8;

1(0^2+0*1+1^2), 3(1^1+1*1+1^2), 9;

1(0^2+0*1+1^2), 2, 5, 10;

1(0^2+0*1+1^2), 11;

1(0^2+0*1+1^2), 2, 3(1^1+1*1+1^2), 4(0^2+0*2+2^2), 6, 12(2^2+2*2+2^2);

1(0^2+0*1+1^2), 13(1^2+1*3+3^2);

1(0^2+0*1+1^2), 2, 7(1^1+1*2+2^2), 14;

1(0^2+0*1+1^1), 3(1^11+1*1+1^2), 5, 15,

i.e. a(1)=2, a(2)=5, a(3)=6, a(4)=8, a(5)=11, a(6)=14, a(7)=15.

MAPLE

isA003136 := proc(n)

    local x, y ;

    for x from 0 do

        if x^2 > n then

            return false;

        end if;

        for y from 0 do

            if x^2+x*y+y^2 = n then

                return true;

            elif x^2+x*y+y^2 > n then

                break;

            end if;

        end do:

    end do:

end proc:

isA230902 := proc(n)

    local a36, a20, d ;

    a36 := 0 ;

    a20 := 0 ;

    for d in numtheory[divisors](n) do

        if isA003136(d) then

            a36 := a36+1 ;

        else

            a20 := a20+1 ;

        end if;

    end do:

    simplify( a36=a20) ;

end proc:

for n from 0 to 200 do

    if isA230902(n) then

    printf("%d, ", n);

    end if;

end do: # R. J. Mathar, Nov 08 2013

CROSSREFS

Cf. A027750, A230851. Subsequence of A000037.

Sequence in context: A214642 A026179 A300063 * A243680 A280381 A105107

Adjacent sequences:  A230899 A230900 A230901 * A230903 A230904 A230905

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Oct 31 2013

EXTENSIONS

Corrected by R. J. Mathar, Nov 08 2013

STATUS

approved

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)