A182469 Triangle read by rows in which row n lists the odd divisors of n.

1, 1, 1, 3, 1, 1, 5, 1, 3, 1, 7, 1, 1, 3, 9, 1, 5, 1, 11, 1, 3, 1, 13, 1, 7, 1, 3, 5, 15, 1, 1, 17, 1, 3, 9, 1, 19, 1, 5, 1, 3, 7, 21, 1, 11, 1, 23, 1, 3, 1, 5, 25, 1, 13, 1, 3, 9, 27, 1, 7, 1, 29, 1, 3, 5, 15, 1, 31, 1, 1, 3, 11, 33, 1, 17, 1, 5, 7, 35, 1

Offset

1,4

Comments

n-th row = intersection of A005408 and of n-th row of A027750.

Links

Reinhard Zumkeller, Rows n = 1..2500 of triangle, flattened

Formula

T(n,k) = A027750(A000265(n),k), 1 <= k <= A001227(n).

A000265(n) = T(n,A001227(n)).

Example

The triangle begins:
.  1   {1}
.  2   {1}
.  3   {1,3}
.  4   {1}
.  5   {1,5}
.  6   {1,3}
.  7   {1,7}
.  8   {1}
.  9   {1,3,9}
. 10   {1,5}
. 11   {1,11}
. 12   {1,3}
. 13   {1,13}
. 14   {1,7}
. 15   {1,3,5,15}
. 16   {1} .

Mathematica

Flatten[Table[Select[Divisors[n], OddQ], {n, 40}]] (* Harvey P. Dale, Aug 13 2012 *)
Flatten[Table[Divisors[n / 2^IntegerExponent[n, 2]], {n, 40}]] (* Amiram Eldar, May 02 2025 *)

Prog

(Haskell)
a182469 n k = a182469_tabf !! (n-1) !! (k-1)
a182469_row = a027750_row . a000265
a182469_tabf = map a182469_row [1..]
(PARI) tabf(nn) = {for (n=1, nn, fordiv(n, d, if (d%2, print1(d, ", "))); print(); ); } \\ Michel Marcus, Apr 22 2017
(PARI) row(n) = divisors(n >> valuation(n, 2)); \\ Amiram Eldar, May 02 2025
(Python)
from sympy import divisors
def row(n):
    return [d for d in divisors(n) if d % 2]
for n in range(1, 21): print(row(n)) # Indranil Ghosh, Apr 22 2017

Crossrefs

Cf. A001227 (row lengths), A000593 (row sums), A136655 (row products).

Cf. A000265, A005408, A027750, A050999, A051000, A037283, A037284, A037285, A171565.

Cf. also A237048.

Sequence in context: A046230 A046229 A255670 * A379634 A329984 A261697

Adjacent sequences: A182466 A182467 A182468 * A182470 A182471 A182472

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Apr 30 2012

Status

approved