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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 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

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