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A359231
a(n) is the smallest centered triangular number divisible by exactly n centered triangular numbers.
1
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
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