A247795 Irregular triangle read by rows in which row n lists the parities of the divisors of n.

1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1

Offset

1

Comments

A001227(n) = number of ones in row n;

A183063(n) = number of zeros in row n.

Links

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

Formula

T(n,k) = A027750(n,k) mod 2, 1 <= k <= A000005(n).

T(n,1) = 1; T(n,A000005(n)) = n mod 2.

a(j) = A000035(A027750(j)), j >= 1. - Omar E. Pol, Feb 20 2022

Example

.   n |  T(n,*)            |  A027750(n,*)           |  A000005(n)
.  ---+--------------------+-------------------------+------------
.   1 |  1                 |  1                      |        1
.   2 |  1  0              |  1   2                  |        2
.   3 |  1  1              |  1   3                  |        2
.   4 |  1  0  0           |  1   2   4              |        3
.   5 |  1  1              |  1   5                  |        2
.   6 |  1  0  1  0        |  1   2   3   6          |        4
.   7 |  1  1              |  1   7                  |        2
.   8 |  1  0  0  0        |  1   2   4   8          |        4
.   9 |  1  1  1           |  1   3   9              |        3
.  10 |  1  0  1  0        |  1   2   5  10          |        4
.  11 |  1  1              |  1  11                  |        2
.  12 |  1  0  1  0  0  0  |  1   2   3   4   6  12  |        6
.  13 |  1  1              |  1  13                  |        2
.  14 |  1  0  1  0        |  1   2   7  14          |        4
.  15 |  1  1  1  1        |  1   3   5  15          |        4
.  16 |  1  0  0  0  0     |  1   2   4   8  16      |        5
.  17 |  1  1              |  1  17                  |        2
.  18 |  1  0  1  0  1  0  |  1   2   3   6   9  18  |        6
.  19 |  1  1              |  1  19                  |        2
.  20 |  1  0  0  1  0  0  |  1   2   4   5  10  20  |        6  .

Prog

(Haskell)
a247795 n k = a247795_tabf !! (n-1) !! (k-1)
a247795_row n = a247795_tabf !! (n-1)
a247795_tabf = map (map (flip mod 2)) a027750_tabf
(PARI) row(n) = apply(x->x%2, divisors(n)); \\ Michel Marcus, Jan 23 2022

Crossrefs

Cf. A000005 (row lengths), A000035, A001227 (row sums), A027750, A183063.

Sequence in context: A305994 A030302 A051023 * A030657 A249066 A176178

Adjacent sequences: A247792 A247793 A247794 * A247796 A247797 A247798

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Sep 28 2014

Status

approved