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

1,2

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.

Links

Table of n, a(n) for n=1..64.

Index entries for sequences that are permutations of the natural numbers

Example

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, ...
  ...

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 *)

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.

Sequence in context: A024635 A217679 A248901 * A037400 A080695 A239448

Adjacent sequences: A280846 A280847 A280848 * A280850 A280851 A280852

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 15 2017

Status

approved