A163870 Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.

2, 2, 3, 2, 4, 3, 2, 5, 2, 3, 4, 6, 2, 7, 3, 5, 2, 4, 8, 2, 3, 6, 9, 2, 4, 5, 10, 3, 7, 2, 11, 2, 3, 4, 6, 8, 12, 5, 2, 13, 3, 9, 2, 4, 7, 14, 2, 3, 5, 6, 10, 15, 2, 4, 8, 16, 3, 11, 2, 17, 5, 7, 2, 3, 4, 6, 9, 12, 18, 2, 19, 3, 13, 2, 4, 5, 8, 10, 20, 2, 3, 6, 7, 14, 21, 2, 4, 11, 22, 3, 5, 9, 15, 2, 23

Offset

1,1

Comments

Row n contains row A002808(n) of table A027750.

T(n,k) = A027751(A002808(n),k+1), k = 1..A144925(n). - Reinhard Zumkeller, Mar 29 2014

Links

Reinhard Zumkeller, Rows n = 1..1000 of table, flattened

Example

The table starts in row n=1 (with the composite 4) as
  2;
  2,3;
  2,4;
  3;
  2,5;
  2,3,4,6;
  2,7;
  3,5;
  2,4,8;
  2,3,6,9;
  2,4,5,10.

Mathematica

Divisors[Select[Range[50], CompositeQ]][[All, 2 ;; -2]] (* Paolo Xausa, Dec 26 2024 *)

Prog

(Haskell)
a163870 n k = a163870_tabf !! (n-1) !! (k-1)
a163870_row n = a163870_tabf !! (n-1)
a163870_tabf = filter (not . null) $ map tail a027751_tabf
-- Reinhard Zumkeller, Mar 29 2014
(Python)
from itertools import islice
def g():
    n, j = 1, 2
    while True:
        n = (n << 1) | 1
        p = 1
        for k in range(2, (j >> 1) + 1):
            p = (p << 1) | 1
            if n % p == 0: yield k
        j+=1
print(list(islice(g(), 95))) # Darío Clavijo, Dec 16 2024

Crossrefs

Cf. A002808, A027750.

Cf. A144925 (row lengths), A062825 (row sums), A056608 (left edge), A160180 (right edge).

Sequence in context: A341285 A263323 A263297 * A327664 A155043 A337327

Adjacent sequences: A163867 A163868 A163869 * A163871 A163872 A163873

Keyword

nonn,tabf

Author

Juri-Stepan Gerasimov, Aug 06 2009

Extensions

Entries checked by R. J. Mathar, Sep 22 2009

Status

approved