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A245717 Triangle read by rows: T(n,k) = gcd(n,k^2), 1 <= k <= n. 4

%I #12 Nov 05 2022 20:07:08

%S 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,

%T 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,

%U 4,3,4,1,12,1,4,3,4,1,12,1,1,1,1,1,1,1,1,1,1,1,1,13

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

%H Reinhard Zumkeller, <a href="/A245717/b245717.txt">Rows n = 1..125 of triangle, flattened</a>

%e First rows and their sums (A078430):

%e . 1: 1 1

%e . 2: 1, 2 3

%e . 3: 1, 1, 3 5

%e . 4: 1, 4, 1, 4 10

%e . 5: 1, 1, 1, 1, 5 9

%e . 6: 1, 2, 3, 2, 1, 6 15

%e . 7: 1, 1, 1, 1, 1, 1, 7 13

%e . 8: 1, 4, 1, 8, 1, 4, 1, 8 28

%e . 9: 1, 1, 9, 1, 1, 9, 1, 1, 9 33

%e . 10: 1, 2, 1, 2, 5, 2, 1, 2, 1, 10 27

%e . 11: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11 21

%e . 12: 1, 4, 3, 4, 1, 12, 1, 4, 3, 4, 1, 12 50

%t Table[GCD[n,k^2],{n,15},{k,n}]//Flatten (* _Harvey P. Dale_, Nov 05 2022 *)

%o (Haskell)

%o a245717 n k = a245717_tabl !! (n-1) !! (k-1)

%o a245717_row n = a245717_tabl !! (n-1)

%o a245717_tabl = zipWith (zipWith gcd) a002024_tabl a133819_tabl

%o (PARI) row(n) = vector(n, k, gcd(n, k^2)); \\ _Michel Marcus_, Jan 24 2022

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

%K nonn,tabl

%O 1,3

%A _Reinhard Zumkeller_, Jul 30 2014

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)