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

1,2

Comments

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

Links

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Centered Triangular Number

Index entries for sequences related to divisors of numbers

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A194501 A348315 A053923 * A326868 A211214 A372813

Adjacent sequences: A359228 A359229 A359230 * A359232 A359233 A359234

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 22 2022

Extensions

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

Status

approved