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A193829 Irregular triangle read by rows in which row n lists the differences between consecutive divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A097865 A105245 A105246 * A198069 A300792 A132082

Adjacent sequences:  A193826 A193827 A193828 * A193830 A193831 A193832

KEYWORD

nonn,tabf,easy

AUTHOR

Omar E. Pol, Aug 31 2011

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)