A081619 - OEIS

%I #24 Jul 07 2023 14:47:48

%S 1,4,9,12,18,20,25,28,32,44,45,48,49,50,52,63,68,75,76,80,92,98,99,

%T 112,116,117,121,124,144,147,148,153,162,164,169,171,172,175,176,188,

%U 207,208,212,236,242,243,244,245,261,268,272,275,279,284,289,292,304,316

%N Numbers whose divisors can be arranged as equilateral triangle.

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

%C Unit together with natural numbers n with number of nontrivial divisors equal to a perfect power. - _Juri-Stepan Gerasimov_, Oct 30 2009

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

%H Reinhard Zumkeller, <a href="/A081619/b081619.txt">Table of n, a(n) for n = 1..10000</a>

%F A010054(A000005(n)) = 1. - _Reinhard Zumkeller_, Jul 12 2013

%e n = 48, A000005(48) = 10, A010054(10) = 1 or A000217(4) = 10:

%e .            1

%e .          2   3

%e .        4   6   8

%e .     12  16  24  48     therefore 48 is a term: a(12) = 48;

%e n = 144, A000005(144) = 15, A010054(15) = 1 or A000217(5) = 15:

%e .             1

%e .           2   3

%e .         4   6   8

%e .       9  12  16  18

%e .    24  36  48  72  144    therefore 48 is a term: a(29) = 144.

%o (Haskell)

%o a081619 n = a081619_list !! (n-1)

%o a081619_list = filter ((== 1) . a010054 . a000005) [1..]

%o -- _Reinhard Zumkeller_, Jul 12 2013

%o (PARI) is(n)=ispolygonal(numdiv(n),3) \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A000027, A001694, A081619, A144925.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 24 2003

%E Example revised and extended by _Reinhard Zumkeller_, Jul 12 2013