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A305995 Rectangular array, by 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. 6
1, 10, 2, 65, 68, 3, 130, 520, 6, 4, 260, 1768, 15, 40, 5, 340, 2600, 30, 104, 50, 12, 1105, 6760, 60, 1040, 1700, 120, 7, 1972, 17680, 150, 20560, 3250, 312, 14, 8, 2210, 62600, 195, 35360, 7825, 600, 35, 2080, 9, 4420, 165896, 204, 85280, 27625, 3120, 70, 4112, 18, 20 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

Northwest corner:

   1    10    65   130    260     340    1105

   2    68   520  1768   2600    6760   17680

   3     6    15    30     60     150     195

   4    40   104  1040  20560   35360   85280

   5    50  1700  3250   7825   27625   31300

  12   120   312   600   3120   61680  106080

   7    14    35    70    140     175     350

   8  2080  4112  6560  32800   38048   52000

   9    18    90   369    585     612     738

MATHEMATICA

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

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

d = Denominator[s];

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

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

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

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

CROSSREFS

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

Sequence in context: A232590 A094715 A213555 * A096043 A001202 A054841

Adjacent sequences:  A305992 A305993 A305994 * A305996 A305997 A305998

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 16 2018

STATUS

approved

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Last modified May 22 14:32 EDT 2019. Contains 323480 sequences. (Running on oeis4.)