A305995 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.

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

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