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

1,3

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, ...

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A310506 A310507 A334115 * A223961 A224391 A224024

Adjacent sequences: A265007 A265008 A265009 * A265011 A265012 A265013

Keyword

nonn

Author

R. J. Mathar, Nov 30 2015

Status

approved