%I #18 Sep 17 2023 10:06:30

%S 1,3,1,0,3,1,3,15,0,1,6,3,6,15,1,0,78,21,10,6,1,3,45,190,0,3,55,1,15,

%T 10,15,28203,45,105,3,1,465,120,55,3,21,15,21,3570,1,6,210,861,0,6,3,

%U 15,105,21945,1,21,3,66,26565,91,276,378,6,0,1596,1,300

%N a(n) = least triangular number t > 0 such that n*t is a triangular number, or 0 if no such t exists.

%C a(n) = 1 if and only if n is a triangular number.

%C Indices of conjectured 0's: 4, 9, 16, 25, 49, 64, 81, 121, 144, 169, 225, 256, 289, 361, 400, 441, 529, 576, 625, 729, ... These are squares of 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27.

%C a(n) = 0 if n = p^(2*j) where p is a prime and j > 0. - _Jon E. Schoenfield_, Sep 17 2023

%e a(614) = 13964154294535688630985 = A000217(167117648945) because 614 * a(614) = A000217(4141012131555), and none of the smaller triangular numbers t satisfies 614*t = A000217(m) for some m.

%Y Cf. A166478 (indices of t in A000217), A225502, A225503.

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Jun 29 2013

%E a(1)-a(25) and a(49)-a(67) from _Jon E. Schoenfield_, Sep 17 2023