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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A024635 A217679 A248901 * A037400 A080695 A239448
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Feb 15 2017
STATUS
approved

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)