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