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

Author

Reinhard Zumkeller, Mar 24 2003

Keywords

• nonn

Comments

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

Unit together with natural numbers n with number of nontrivial divisors equal to a perfect power. - Juri-Stepan Gerasimov, Oct 30 2009

This is wrong, e.g. a(29)=144, A000005(144)=15 and A075802(15-2)=0, see also example. - Reinhard Zumkeller, Jul 12 2013

Examples

			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.
		

Links

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

Crossrefs

Cf. A000027, A001694, A081619, A144925.

Programs

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

Formula

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

Extensions

Example revised and extended by Reinhard Zumkeller, Jul 12 2013