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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
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