cp's OEIS Frontend

A152005 Numbers whose square is the product of two distinct tetrahedral numbers A000292.

%I A152005 #31 Jan 18 2024 09:58:51
%S A152005 2,140,280,1092,166460,189070,665840,804540,845460,34250920,38336088,
%T A152005 133784560,138535992,225792840,4998790160,6301258040,7559616818,
%U A152005 8367691640,39991371446,104637102152,227490888350,1497809326860,296523233581822
%N A152005 Numbers whose square is the product of two distinct tetrahedral numbers A000292.
%C A152005 There may be values that are not given in the recurrence shown. This sequence is suggested by Ulas, p. 11, who supplied the recurrence.
%C A152005 a(24) > 3*10^14. - _Donovan Johnson_, Jan 11 2012
%H A152005 Maciej Ulas, <a href="http://arxiv.org/abs/0811.2477">On certain Diophantine equations related to triangular and tetrahedral numbers</a>, arXiv:0811.2477 [math.NT], 2008.
%F A152005 a(n) = T(i)*T(j) where T(k) = A000292(k) = C(k+2,3) = k*(k+1)*(k+2)/6.
%e A152005 From _R. J. Mathar_, Jan 22 2009: (Start)
%e A152005 2 is in the sequence because 2^2 = 4*1 = T(2)*T(1).
%e A152005 140 is in the sequence 140^2 = 560*35 = T(14)*T(5) = 19600*1 = T(48)*T(1).
%e A152005 280 is in the sequence because 280^2 = 19600*4 = T(48)*T(2).
%e A152005 1092 is in the sequence because 1092^2 = 3276*364 = T(26)*T(12). (End)
%t A152005 (* This program is not suitable to compute more than a dozen terms. *)
%t A152005 terms = 12; imin = 1; imax = 3000;
%t A152005 Union[Reap[Do[k2 = i(i+1)(i+2)/6 j(j+1)(j+2)/6; k = Sqrt[k2]; If[IntegerQ[k], Print[k]; Sow[k]], {i, imin, imax}, {j, i+1, imax}]][[2, 1]]][[1 ;; terms]] (* _Jean-François Alcover_, Oct 31 2018 *)
%Y A152005 Cf. A000292, A175497 (products distinct triangular numbers).
%K A152005 nonn,more
%O A152005 1,1
%A A152005 _Jonathan Vos Post_, Nov 19 2008
%E A152005 Sequence replaced by sequence with no intermediate terms missing by _R. J. Mathar_, Jan 22 2009
%E A152005 a(15)-a(18) from _Donovan Johnson_, Jan 24 2009
%E A152005 a(19)-a(23) from _Donovan Johnson_, Jan 11 2012