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Irregular triangle read by rows in which row n lists the parities of the divisors of n.
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%I #13 Mar 13 2022 19:03:06

%S 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,

%T 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,

%U 1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,1,1

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

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

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

%H Reinhard Zumkeller, <a href="/A247795/b247795.txt">Rows n = 1..1000 of triangle, flattened</a>

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

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

%F a(j) = A000035(A027750(j)), j >= 1. - _Omar E. Pol_, Feb 20 2022

%e . n | T(n,*) | A027750(n,*) | A000005(n)

%e . ---+--------------------+-------------------------+------------

%e . 1 | 1 | 1 | 1

%e . 2 | 1 0 | 1 2 | 2

%e . 3 | 1 1 | 1 3 | 2

%e . 4 | 1 0 0 | 1 2 4 | 3

%e . 5 | 1 1 | 1 5 | 2

%e . 6 | 1 0 1 0 | 1 2 3 6 | 4

%e . 7 | 1 1 | 1 7 | 2

%e . 8 | 1 0 0 0 | 1 2 4 8 | 4

%e . 9 | 1 1 1 | 1 3 9 | 3

%e . 10 | 1 0 1 0 | 1 2 5 10 | 4

%e . 11 | 1 1 | 1 11 | 2

%e . 12 | 1 0 1 0 0 0 | 1 2 3 4 6 12 | 6

%e . 13 | 1 1 | 1 13 | 2

%e . 14 | 1 0 1 0 | 1 2 7 14 | 4

%e . 15 | 1 1 1 1 | 1 3 5 15 | 4

%e . 16 | 1 0 0 0 0 | 1 2 4 8 16 | 5

%e . 17 | 1 1 | 1 17 | 2

%e . 18 | 1 0 1 0 1 0 | 1 2 3 6 9 18 | 6

%e . 19 | 1 1 | 1 19 | 2

%e . 20 | 1 0 0 1 0 0 | 1 2 4 5 10 20 | 6 .

%o (Haskell)

%o a247795 n k = a247795_tabf !! (n-1) !! (k-1)

%o a247795_row n = a247795_tabf !! (n-1)

%o a247795_tabf = map (map (flip mod 2)) a027750_tabf

%o (PARI) row(n) = apply(x->x%2, divisors(n)); \\ _Michel Marcus_, Jan 23 2022

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

%K nonn,tabf

%O 1

%A _Reinhard Zumkeller_, Sep 28 2014