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).

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

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 A333965

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