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A280849 Square array T(j,k) read by antidiagonals upwards, in which column k lists the numbers n having k odd divisors greater than sqrt(2*n), with j >= 1, k >= 0.

%I A280849 #34 Oct 10 2018 20:05:25
%S A280849 1,2,3,4,5,21,6,7,27,75,8,9,33,135,105,12,10,39,147,189,315,16,11,45,
%T A280849 165,225,525,495,20,13,51,171,297,675,585,945,24,14,55,175,351,693,
%U A280849 765,1155,1575,28,15,57,195,385,735,855,1365,2475,2835,32,17,63,207,405,819,1071,1485,2625
%N A280849 Square array T(j,k) read by antidiagonals upwards, in which column k lists the numbers n having k odd divisors greater than sqrt(2*n), with j >= 1, k >= 0.
%C A280849 Conjecture: column k lists also the numbers n having k pairs of equidistant subparts in the symmetric representation of sigma(n).
%C A280849 For more information about the "subparts" see A279387.
%C A280849 This sequence is a permutation of the natural numbers.
%H A280849 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A280849 The upper-left corner of the square array begins:
%e A280849    1,  3, 21,  75, 105, 315, 495,  945, 1575, 2835, ...
%e A280849    2,  5, 27, 135, 189, 525, 585, 1155, 2475, ...
%e A280849    4,  7, 33, 147, 225, 675, 765, 1365, ...
%e A280849    6,  9, 39, 165, 297, 693, 855, ...
%e A280849    8  10, 45, 171, 351, 735, ...
%e A280849   12, 11, 51, 175, 385, ...
%e A280849   16, 13, 55, 195, ...
%e A280849   20, 14, 57, ...
%e A280849   24, 15, ...
%e A280849   28, ...
%e A280849   ...
%t A280849 jMax = 11; nMax = 5000; cnt[n_] := cnt[n] = DivisorSum[n, Boole[OddQ[#] && # > Sqrt[2n]]&]; col[k_] := Select[Range[nMax], cnt[#] == k&]; T[j_, k_] := col[k][[j]]; Table[T[j-k, k], {j, 1, jMax}, {k, 0, j-1}] // Flatten (* _Jean-François Alcover_, Feb 16 2017 *)
%Y A280849 Row 1 gives A281008.
%Y A280849 Column 0 gives A082662. The rest of the terms are in A281005 in increasing order.
%Y A280849 Cf. A000203, A001227, A067742, A131576, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A244050, A245092, A261699, A262626, A279387, A280940.
%K A280849 nonn,tabl
%O A280849 1,2
%A A280849 _Omar E. Pol_, Feb 15 2017