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.

1, 2, 3, 4, 5, 21, 6, 7, 27, 75, 8, 9, 33, 135, 105, 12, 10, 39, 147, 189, 315, 16, 11, 45, 165, 225, 525, 495, 20, 13, 51, 171, 297, 675, 585, 945, 24, 14, 55, 175, 351, 693, 765, 1155, 1575, 28, 15, 57, 195, 385, 735, 855, 1365, 2475, 2835, 32, 17, 63, 207, 405, 819, 1071, 1485, 2625

Offset: 1

Author

Omar E. Pol, Feb 15 2017

Keywords

• nonn
• tabl

Comments

Conjecture: column k lists also the numbers n having k pairs of equidistant subparts in the symmetric representation of sigma(n).

For more information about the "subparts" see A279387.

This sequence is a permutation of the natural numbers.

Examples

			The upper-left corner of the square array begins:
   1,  3, 21,  75, 105, 315, 495,  945, 1575, 2835, ...
   2,  5, 27, 135, 189, 525, 585, 1155, 2475, ...
   4,  7, 33, 147, 225, 675, 765, 1365, ...
   6,  9, 39, 165, 297, 693, 855, ...
   8  10, 45, 171, 351, 735, ...
  12, 11, 51, 175, 385, ...
  16, 13, 55, 195, ...
  20, 14, 57, ...
  24, 15, ...
  28, ...
  ...
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Row 1 gives A281008.

Column 0 gives A082662. The rest of the terms are in A281005 in increasing order.

Cf. A000203, A001227, A067742, A131576, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A244050, A245092, A261699, A262626, A279387, A280940.

Programs

Mathematica

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 *)