A359231 - OEIS

%I #19 Jan 02 2023 09:01:20

%S 1,4,64,5860,460,74260,14260,1221760,5567104,103360,20120860,

%T 169096960,1211757760,31286787760,31498960,114183284260,1553569960,

%U 33186496960,446613160960,43581101074960,274644405760,64262632960,121634429663260,5786547945760

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

%C a(25) > 10^15. a(30) = 281149511296960. - _Jon E. Schoenfield_, Dec 25 2022

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%e 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.

%o (Magma)

%o // Note: the program below finds all terms through a(22) except for

%o //  a(20) = 43581101074960, which would be reached at k = 5390183.

%o a := [ 0 : n in [ 1 .. 22 ] ];

%o for k in [ 0 .. 550000 ] do

%o    c := 3*((k*(k - 1)) div 2) + 1;

%o    D := Divisors(c);

%o    n := 0;

%o    for d in D do

%o       if d mod 3 eq 1 then

%o          if IsSquare(((d - 1) div 3)*8 + 1) then

%o             n +:= 1;

%o          end if;

%o       end if;

%o    end for;

%o    if a[n] eq 0 then

%o       a[n] := c;

%o    end if;

%o end for;

%o a; // _Jon E. Schoenfield_, Dec 25 2022

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

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 22 2022

%E a(8)-a(24) from _Jon E. Schoenfield_, Dec 25 2022