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A193829
Irregular triangle read by rows in which row n lists the differences between consecutive divisors of n.
30
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
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. A060682 (distinct terms per row), A060680 (row minima), A060681 (row maxima).
Sequence in context: A105245 A105246 A328027 * A337714 A198069 A300792
KEYWORD
nonn,tabf,easy
AUTHOR
Omar E. Pol, Aug 31 2011
STATUS
approved