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A081619 Numbers whose divisors can be arranged as equilateral triangle. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

REFERENCES

Mohammad K. Azarian, A Trigonometric Characterization of  Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96.  Solution published in Vol. 32, No. 1, Winter 1998, pp. 84-85.

Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337.  Solution published in Vol. 29, No. 3, Fall 1995, pp. 324-325.

LINKS

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

FORMULA

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.

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: A089910 A177880 A059269 * A038109 A067259 A060687

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

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Last modified February 17 14:12 EST 2018. Contains 299296 sequences. (Running on oeis4.)