A173395 a(n) = (A002260(n) + 1) * (A004736(n) + 1).

4, 6, 6, 8, 9, 8, 10, 12, 12, 10, 12, 15, 16, 15, 12, 14, 18, 20, 20, 18, 14, 16, 21, 24, 25, 24, 21, 16, 18, 24, 28, 30, 30, 28, 24, 18, 20, 27, 32, 35, 36, 35, 32, 27, 20, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 26

Offset

1,1

Comments

Every number of this sequence is composite, and every composite number appears in this sequence.

Viewed as a square array this sequence is the multiplication table with headers starting at 2: A002260 and A004736 being indexing functions for square arrays, a(n)=T(i,j) with i=A002260(n) and j=A004736(n), T(i,j)=(i+1)(j+1). - Luc Rousseau, Oct 15 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150).

Michael Somos, Sequences used for indexing triangular or square arrays.

Formula

a(n) = ((2 n + round(sqrt(2n)) - round(sqrt(2n))^2)/2 + 1)((2 - 2n + round(sqrt(2n)) + round(sqrt(2n))^2)/2 + 1).

Example

4;
6,6;
8,9,8;
10,12,12,10;
12,15,16,15,12;
From Luc Rousseau, Oct 15 2017: (Start)
Viewed as a square array,
   4  6  8 10 12 ...
   6  9 12 15 18 ...
   8 12 16 20 24 ...
  10 15 20 25 30 ...
  12 18 24 30 36 ...
  ...
= the multiplication table with headers starting at 2.
(End)

Mathematica

Map[Times @@ # & /@ Transpose@{#, Reverse@ #} &, Array[Range, 12] + 1] // Flatten (* Michael De Vlieger, Oct 16 2017 *)

Prog

(Other) a(n) = (1/2 (2 n+Round[sqrt(2 n)]-Round[sqrt(2 n)]^2)+1) (1/2 (2-2 n+Round[sqrt(2 n)]+Round[sqrt(2 n)]^2)+1)
(PARI) a(n) = ((2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2 + 1)*((2 - 2*n + round(sqrt(2*n)) + round(sqrt(2*n))^2)/2 + 1) \\ Michel Marcus, Jun 19 2013
(PARI) a(n)=my(s=round(sqrt(n*=2))); (n-s-s^2-4)*(n+s-s^2+2)/4 \\ Charles R Greathouse IV, Jun 19 2013

Crossrefs

Cf. A002260, A004736.

Sequence in context: A111653 A228363 A334289 * A305317 A049089 A028327

Adjacent sequences: A173392 A173393 A173394 * A173396 A173397 A173398

Keyword

nonn,easy,tabl

Author

Fabio Civolani (civox(AT)tiscali.it), Feb 17 2010

Status

approved