OFFSET
1,2
COMMENTS
a(25) > 10^15. a(30) = 281149511296960. - Jon E. Schoenfield, Dec 25 2022
LINKS
Eric Weisstein's World of Mathematics, Centered Triangular Number
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 22 2022
EXTENSIONS
a(8)-a(24) from Jon E. Schoenfield, Dec 25 2022
STATUS
approved