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A193829 Irregular triangle read by rows in which row n lists the differences between consecutive divisors of n.

%I A193829 #33 Jun 25 2015 16:13:00
%S A193829 1,2,1,2,4,1,1,3,6,1,2,4,2,6,1,3,5,10,1,1,1,2,6,12,1,5,7,2,2,10,1,2,4,
%T A193829 8,16,1,1,3,3,9,18,1,2,1,5,10,2,4,14,1,9,11,22,1,1,1,2,2,4,12,4,20,1,
%U A193829 11,13,2,6,18,1,2,3,7,14,28,1,1,2,1,4,5,15,30
%N A193829 Irregular triangle read by rows in which row n lists the differences between consecutive divisors of n.
%C A193829 The sum of row n gives A000027(n-1). The product of row n gives A057449(n). Row n has length A032741(n). The final term of row n is A060681(n). It appears that the first term of row n is A057237(n).
%H A193829 Alois P. Heinz, <a href="/A193829/b193829.txt">Rows n = 2..1600, flattened</a>
%H A193829 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv05.jpg">Illustration of divisors of n</a>
%H A193829 Wikipedia, <a href="http://en.wikipedia.org/wiki/Table_of_divisors">Table of divisors</a>
%F A193829 T(n,k) = A027750(n,k+1)-A027750(n,k). - R. J. Mathar, Sep 01 2011
%e A193829 Written as a triangle:
%e A193829 1,
%e A193829 2,
%e A193829 1, 2,
%e A193829 4,
%e A193829 1, 1, 3,
%e A193829 6,
%e A193829 1, 2, 4,
%e A193829 2, 6,
%e A193829 1, 3, 5,
%e A193829 10,
%e A193829 1, 1, 1, 2, 6
%t A193829 Flatten[Table[Differences[Divisors[n]], {n, 2, 30}]] (* _T. D. Noe_, Aug 31 2011 *)
%o A193829 (Haskell)
%o A193829 import Data.List (genericIndex)
%o A193829 a193829 n k = genericIndex a193829_tabf (n - 1) !! (k - 1)
%o A193829 a193829_row n = genericIndex a193829_tabf (n - 1)
%o A193829 a193829_tabf = zipWith (zipWith (-))
%o A193829                        (map tail a027750_tabf') a027750_tabf'
%o A193829 -- _Reinhard Zumkeller_, Jun 25 2015, Jun 23 2013
%Y A193829 Cf. A027750, A032742.
%Y A193829 Cf. A060682 (distinct terms per row), A060680 (row minima), A060681 (row maxima).
%K A193829 nonn,tabf,easy
%O A193829 2,2
%A A193829 _Omar E. Pol_, Aug 31 2011