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A182469 Triangle read by rows in which row n lists the odd divisors of n.

%I A182469 #40 May 02 2025 03:31:13
%S A182469 1,1,1,3,1,1,5,1,3,1,7,1,1,3,9,1,5,1,11,1,3,1,13,1,7,1,3,5,15,1,1,17,
%T A182469 1,3,9,1,19,1,5,1,3,7,21,1,11,1,23,1,3,1,5,25,1,13,1,3,9,27,1,7,1,29,
%U A182469 1,3,5,15,1,31,1,1,3,11,33,1,17,1,5,7,35,1
%N A182469 Triangle read by rows in which row n lists the odd divisors of n.
%C A182469 n-th row = intersection of A005408 and of n-th row of A027750.
%H A182469 Reinhard Zumkeller, <a href="/A182469/b182469.txt">Rows n = 1..2500 of triangle, flattened</a>
%F A182469 T(n,k) = A027750(A000265(n),k), 1 <= k <= A001227(n).
%F A182469 A000265(n) = T(n,A001227(n)).
%e A182469 The triangle begins:
%e A182469 .  1   {1}
%e A182469 .  2   {1}
%e A182469 .  3   {1,3}
%e A182469 .  4   {1}
%e A182469 .  5   {1,5}
%e A182469 .  6   {1,3}
%e A182469 .  7   {1,7}
%e A182469 .  8   {1}
%e A182469 .  9   {1,3,9}
%e A182469 . 10   {1,5}
%e A182469 . 11   {1,11}
%e A182469 . 12   {1,3}
%e A182469 . 13   {1,13}
%e A182469 . 14   {1,7}
%e A182469 . 15   {1,3,5,15}
%e A182469 . 16   {1} .
%t A182469 Flatten[Table[Select[Divisors[n],OddQ],{n,40}]] (* _Harvey P. Dale_, Aug 13 2012 *)
%t A182469 Flatten[Table[Divisors[n / 2^IntegerExponent[n, 2]], {n, 40}]] (* _Amiram Eldar_, May 02 2025 *)
%o A182469 (Haskell)
%o A182469 a182469 n k = a182469_tabf !! (n-1) !! (k-1)
%o A182469 a182469_row = a027750_row . a000265
%o A182469 a182469_tabf = map a182469_row [1..]
%o A182469 (PARI) tabf(nn) = {for (n=1, nn, fordiv(n, d, if (d%2, print1(d, ", "))); print(););} \\ _Michel Marcus_, Apr 22 2017
%o A182469 (PARI) row(n) = divisors(n >> valuation(n, 2)); \\ _Amiram Eldar_, May 02 2025
%o A182469 (Python)
%o A182469 from sympy import divisors
%o A182469 def row(n):
%o A182469     return [d for d in divisors(n) if d % 2]
%o A182469 for n in range(1, 21): print(row(n)) # _Indranil Ghosh_, Apr 22 2017
%Y A182469 Cf. A001227 (row lengths), A000593 (row sums), A136655 (row products).
%Y A182469 Cf. A000265, A005408, A027750, A050999, A051000, A037283, A037284, A037285, A171565.
%Y A182469 Cf. also A237048.
%K A182469 nonn,tabf
%O A182469 1,4
%A A182469 _Reinhard Zumkeller_, Apr 30 2012