A081619 Numbers whose divisors can be arranged as equilateral triangle.

1, 4, 9, 12, 18, 20, 25, 28, 32, 44, 45, 48, 49, 50, 52, 63, 68, 75, 76, 80, 92, 98, 99, 112, 116, 117, 121, 124, 144, 147, 148, 153, 162, 164, 169, 171, 172, 175, 176, 188, 207, 208, 212, 236, 242, 243, 244, 245, 261, 268, 272, 275, 279, 284, 289, 292, 304, 316

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A000005(a(n)) = A000217(m) for some m; A000005(A081620(n))=n*(n+1)/2.

A010054(A000005(n)) = 1. - Reinhard Zumkeller, Jul 12 2013

Example

n = 48, A000005(48) = 10, A010054(10) = 1 or A000217(4) = 10:
            1
          2   3
        4   6   8
     12  16  24  48     therefore 48 is a term: a(12) = 48;
n = 144, A000005(144) = 15, A010054(15) = 1 or A000217(5) = 15:
             1
           2   3
         4   6   8
       9  12  16  18
    24  36  48  72  144    therefore 48 is a term: a(29) = 144.

Mathematica

A081619Q[k_] := IntegerQ[Sqrt[8*DivisorSigma[0, k] + 1]];
Select[Range[500], A081619Q] (* Paolo Xausa, Nov 05 2025 *)

Prog

(Haskell)
a081619 n = a081619_list !! (n-1)
a081619_list = filter ((== 1) . a010054 . a000005) [1..]
-- Reinhard Zumkeller, Jul 12 2013
(PARI) is(n)=ispolygonal(numdiv(n), 3) \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A000027, A001694, A081619, A144925.

Sequence in context: A177880 A059269 A369209 * A377562 A336594 A304365

Adjacent sequences: A081616 A081617 A081618 * A081620 A081621 A081622

Keyword

nonn

Author

Reinhard Zumkeller, Mar 24 2003

Extensions

Example revised and extended by Reinhard Zumkeller, Jul 12 2013

Status

approved