A245717 Triangle read by rows: T(n,k) = gcd(n,k^2), 1 <= k <= n.

1, 1, 2, 1, 1, 3, 1, 4, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 2, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 4, 1, 8, 1, 4, 1, 8, 1, 1, 9, 1, 1, 9, 1, 1, 9, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 4, 3, 4, 1, 12, 1, 4, 3, 4, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13

Offset

1,3

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Example

First rows and their sums (A078430):
.    1:   1                                           1
.    2:   1, 2                                        3
.    3:   1, 1, 3                                     5
.    4:   1, 4, 1, 4                                 10
.    5:   1, 1, 1, 1, 5                               9
.    6:   1, 2, 3, 2, 1,  6                          15
.    7:   1, 1, 1, 1, 1,  1, 7                       13
.    8:   1, 4, 1, 8, 1,  4, 1, 8                    28
.    9:   1, 1, 9, 1, 1,  9, 1, 1, 9                 33
.   10:   1, 2, 1, 2, 5,  2, 1, 2, 1, 10             27
.   11:   1, 1, 1, 1, 1,  1, 1, 1, 1,  1, 11         21
.   12:   1, 4, 3, 4, 1, 12, 1, 4, 3,  4,  1, 12     50

Mathematica

Table[GCD[n, k^2], {n, 15}, {k, n}]//Flatten (* Harvey P. Dale, Nov 05 2022 *)

Prog

(Haskell)
a245717 n k = a245717_tabl !! (n-1) !! (k-1)
a245717_row n = a245717_tabl !! (n-1)
a245717_tabl = zipWith (zipWith gcd) a002024_tabl a133819_tabl
(PARI) row(n) = vector(n, k, gcd(n, k^2)); \\ Michel Marcus, Jan 24 2022

Crossrefs

Cf. A050873, A002024, A133819, A078430 (row sums).

Sequence in context: A089141 A336084 A375128 * A248008 A327981 A348447

Adjacent sequences: A245714 A245715 A245716 * A245718 A245719 A245720

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jul 30 2014

Status

approved