

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
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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 upperleft 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[jk, k], {j, 1, jMax}, {k, 0, j1}] // Flatten (* JeanFrançois Alcover, Feb 16 2017 *)


CROSSREFS

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.


KEYWORD



AUTHOR



STATUS

approved



