A265010 Numbers which are the product of two tetrahedral numbers.

0, 1, 4, 10, 16, 20, 35, 40, 56, 80, 84, 100, 120, 140, 165, 200, 220, 224, 286, 336, 350, 364, 400, 455, 480, 560, 660, 680, 700, 816, 840, 880, 969, 1120, 1140, 1144, 1200, 1225, 1330, 1456, 1540, 1650, 1680, 1771, 1820, 1960, 2024, 2200, 2240

Offset: 1

Author

R. J. Mathar, Nov 30 2015

Keywords

• nonn

Comments

This is for the tetrahedral numbers A000292 what A085780 is for the triangular numbers.

The subsequence of numbers with more than one factorization starts 0, 560 (= 65*10 = 1*560), 19600 (= 560*15 = 19600*1), 28560 (=816 *35 = 7140*4), 43680, 292600, 416640, ...

Examples

			Contains 480=4*120, 560=1*560, 660=4*165, 680=1*680, 700=20*35, ....
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085780. Subsequences: A000292, A001249, A027790, A105939, A104474, A104677.

Programs

Maple

# reuses code of A000292
isA265010 := proc(n)
    if n = 0 then
        return true;
    end if;
    for d in numtheory[divisors](n) do
        if isA000292(d) and isA000292(n/d) then
            return true;
        end if;
    end do:
    false;
end proc:
for n from 0 to 4000 do
    if isA265010(n) then
        printf("%d, ",n);
    end if;
end do:

Mathematica

lim = 2240; t = Table[Binomial[n + 2, 3], {n, 0, 10^3}]; f[n_] := Select[{#, n/#} & /@ Select[Divisors[n], # <= Sqrt@ n && MemberQ[t, #] &], MemberQ[t, Last@ #] &]; Select[Range@ lim, Length@ f@ # > 0 &] (* Michael De Vlieger, Nov 30 2015 *)

Formula

{n: n = A000292(i)*A000292(j) for some i,j>=0}.