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

%I A359231 #20 Feb 16 2025 08:34:04
%S A359231 1,4,64,5860,460,74260,14260,1221760,5567104,103360,20120860,
%T A359231 169096960,1211757760,31286787760,31498960,114183284260,1553569960,
%U A359231 33186496960,446613160960,43581101074960,274644405760,64262632960,121634429663260,5786547945760
%N A359231 a(n) is the smallest centered triangular number divisible by exactly n centered triangular numbers.
%C A359231 a(25) > 10^15. a(30) = 281149511296960. - _Jon E. Schoenfield_, Dec 25 2022
%H A359231 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%H A359231 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e A359231 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 A359231 (Magma)
%o A359231 // Note: the program below finds all terms through a(22) except for
%o A359231 //  a(20) = 43581101074960, which would be reached at k = 5390183.
%o A359231 a := [ 0 : n in [ 1 .. 22 ] ];
%o A359231 for k in [ 0 .. 550000 ] do
%o A359231    c := 3*((k*(k - 1)) div 2) + 1;
%o A359231    D := Divisors(c);
%o A359231    n := 0;
%o A359231    for d in D do
%o A359231       if d mod 3 eq 1 then
%o A359231          if IsSquare(((d - 1) div 3)*8 + 1) then
%o A359231             n +:= 1;
%o A359231          end if;
%o A359231       end if;
%o A359231    end for;
%o A359231    if a[n] eq 0 then
%o A359231       a[n] := c;
%o A359231    end if;
%o A359231 end for;
%o A359231 a; // _Jon E. Schoenfield_, Dec 25 2022
%Y A359231 Cf. A005448, A076983, A300409, A358544, A358861, A359232.
%K A359231 nonn
%O A359231 1,2
%A A359231 _Ilya Gutkovskiy_, Dec 22 2022
%E A359231 a(8)-a(24) from _Jon E. Schoenfield_, Dec 25 2022