A359231 a(n) is the smallest centered triangular number divisible by exactly n centered triangular numbers.

1, 4, 64, 5860, 460, 74260, 14260, 1221760, 5567104, 103360, 20120860, 169096960, 1211757760, 31286787760, 31498960, 114183284260, 1553569960, 33186496960, 446613160960, 43581101074960, 274644405760, 64262632960, 121634429663260, 5786547945760

Offset: 1

Author

Ilya Gutkovskiy, Dec 22 2022

Keywords

• nonn

Comments

a(25) > 10^15. a(30) = 281149511296960. - Jon E. Schoenfield, Dec 25 2022

Examples

			a(5) = 460, because 460 is a centered triangular number that has 5 centered triangular divisors {1, 4, 10, 46, 460} and this is the smallest such number.
		

Links

• Eric Weisstein's World of Mathematics, Centered Triangular Number
• Index entries for sequences related to divisors of numbers

Crossrefs

Cf. A005448, A076983, A300409, A358544, A358861, A359232.

Programs

Magma

// Note: the program below finds all terms through a(22) except for
//  a(20) = 43581101074960, which would be reached at k = 5390183.
a := [ 0 : n in [ 1 .. 22 ] ];
for k in [ 0 .. 550000 ] do
   c := 3*((k*(k - 1)) div 2) + 1;
   D := Divisors(c);
   n := 0;
   for d in D do
      if d mod 3 eq 1 then
         if IsSquare(((d - 1) div 3)*8 + 1) then
            n +:= 1;
         end if;
      end if;
   end for;
   if a[n] eq 0 then
      a[n] := c;
   end if;
end for;
a; // Jon E. Schoenfield, Dec 25 2022

Extensions

a(8)-a(24) from Jon E. Schoenfield, Dec 25 2022