cp's OEIS Frontend

A375037 Irregular triangle read by rows T(n,k), n >= 1, k >= 1, in which row n lists the divisors of n but every middle divisor is replaced with zero.

%I A375037 #16 Aug 06 2024 22:01:04
%S A375037 0,0,2,1,3,1,0,4,1,5,1,0,0,6,1,7,1,0,4,8,1,0,9,1,2,5,10,1,11,1,2,0,0,
%T A375037 6,12,1,13,1,2,7,14,1,0,0,15,1,2,0,8,16,1,17,1,2,0,6,9,18,1,19,1,2,0,
%U A375037 0,10,20,1,3,7,21,1,2,11,22,1,23,1,2,3,0,0,8,12,24
%N A375037 Irregular triangle read by rows T(n,k), n >= 1, k >= 1, in which row n lists the divisors of n but every middle divisor is replaced with zero.
%C A375037 The nonzero terms in row n are the nonmiddle divisors of n.
%C A375037 The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).
%e A375037 Triangle begins:
%e A375037   0;
%e A375037   0, 2;
%e A375037   1, 3;
%e A375037   1, 0, 4;
%e A375037   1, 5;
%e A375037   1, 0, 0, 6;
%e A375037   1, 7;
%e A375037   1, 0, 4, 8;
%e A375037   1, 0, 9;
%e A375037   1, 2, 5, 10;
%e A375037   1, 11;
%e A375037   1, 2, 0, 0, 6, 12;
%e A375037   ...
%e A375037 For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors are [3, 4], but here the middle divisors are replaced with zeros, so the 12th row of the triangle is [1, 2, 0, 0, 6, 12].
%t A375037 row[n_] := Divisors[n] /. {x_?(Sqrt[n/2] <= # < Sqrt[2*n] &) -> 0}; Table[row[n], {n, 1, 24}] // Flatten (* _Amiram Eldar_, Jul 29 2024 *)
%Y A375037 Row sums give A302433.
%Y A375037 Nonzero terms give A375038.
%Y A375037 Row lengths give A000005.
%Y A375037 The number of zeros in row n is A067742(n).
%Y A375037 The number of nonzero terms in row n is A067743(n).
%Y A375037 Cf. A000005, A027750, A067742, A299761, A303297.
%K A375037 nonn,tabf,easy
%O A375037 1,3
%A A375037 _Omar E. Pol_, Jul 28 2024