A305995 - OEIS

%I #9 Oct 31 2019 01:43:00

%S 1,10,2,65,68,3,130,520,6,4,260,1768,15,40,5,340,2600,30,104,50,12,

%T 1105,6760,60,1040,1700,120,7,1972,17680,150,20560,3250,312,14,8,2210,

%U 62600,195,35360,7825,600,35,2080,9,4420,165896,204,85280,27625,3120,70,4112,18,20

%N Rectangular array read by downward antidiagonals; row n consists of the numbers m such that n is the denominator of d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1), where d(1),d(2),...,d(k) are the unitary divisors of m.

%C Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers. The numbers in row n are divisible by n; see A305996 for the quotients.

%e Northwest corner:

%e    1    10    65   130    260     340    1105

%e    2    68   520  1768   2600    6760   17680

%e    3     6    15    30     60     150     195

%e    4    40   104  1040  20560   35360   85280

%e    5    50  1700  3250   7825   27625   31300

%e   12   120   312   600   3120   61680  106080

%e    7    14    35    70    140     175     350

%e    8  2080  4112  6560  32800   38048   52000

%e    9    18    90   369    585     612     738

%t t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];

%t s = Table[Total[t[n]], {n, 1, z}]; a[n_] := If[IntegerQ[s[[n]]], 1, 0];

%t d = Denominator[s];

%t row[n_] := Flatten[Position[d, n]]

%t TableForm[Table[row[n], {n, 1, 10}]]  (* A305995 array *)

%t r1[n_, k_] := row[n][[k]]; zz = 10;

%t Flatten[Table[r1[n - k + 1, k], {n, zz}, {k, n, 1, -1}]]  (* A305995 sequence *)

%Y Cf. A077610, A229994, A229996, A229997, A229998, A229998, A305996.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jun 16 2018