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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: A312862 A177880 A059269 * A336594 A304365 A038109 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 October 4 20:31 EDT 2022. Contains 357240 sequences. (Running on oeis4.)