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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 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.)