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

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, 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, 11, 13, 2, 6, 18, 1, 2, 3, 7, 14, 28, 1, 1, 2, 1, 4, 5, 15, 30

Offset

2,2

Comments

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).

Links

Alois P. Heinz, Rows n = 2..1600, flattened

Omar E. Pol, Illustration of divisors of n

Wikipedia, Table of divisors

Formula

T(n,k) = A027750(n,k+1)-A027750(n,k). - R. J. Mathar, Sep 01 2011

Example

Written as a triangle:
1,
2,
1, 2,
4,
1, 1, 3,
6,
1, 2, 4,
2, 6,
1, 3, 5,
10,
1, 1, 1, 2, 6

Mathematica

Flatten[Table[Differences[Divisors[n]], {n, 2, 30}]] (* T. D. Noe, Aug 31 2011 *)

Prog

(Haskell)
import Data.List (genericIndex)
a193829 n k = genericIndex a193829_tabf (n - 1) !! (k - 1)
a193829_row n = genericIndex a193829_tabf (n - 1)
a193829_tabf = zipWith (zipWith (-))
                       (map tail a027750_tabf') a027750_tabf'
-- Reinhard Zumkeller, Jun 25 2015, Jun 23 2013

Crossrefs

Cf. A027750, A032742.

Cf. A060682 (distinct terms per row), A060680 (row minima), A060681 (row maxima).

Sequence in context: A105245 A105246 A328027 * A337714 A198069 A300792

Adjacent sequences: A193826 A193827 A193828 * A193830 A193831 A193832

Keyword

nonn,tabf,easy

Author

Omar E. Pol, Aug 31 2011

Status

approved