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
Keywords
Examples
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.
Links
- Eric Weisstein's World of Mathematics, Centered Triangular Number
- Index entries for sequences related to divisors of numbers
Programs
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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
Extensions
a(8)-a(24) from Jon E. Schoenfield, Dec 25 2022
Comments