A161205 Triangle read by rows in which row n lists 2n-1 followed by 2n numbers 2n.

1, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16

Offset

1,2

Comments

Row sums: A125202(n+1). - R. J. Mathar, Feb 16 2010

Links

Table of n, a(n) for n=1..72.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Omar E. Pol, Illustration: Divisors and pi(x)

Formula

If n is a perfect square, then a(n) = 2*sqrt(n)-1; otherwise a(n) = 2*floor(sqrt(n)). - Nathaniel Johnston, May 06 2011

a(n) = A000196(n-1) + A000196(n) = floor(sqrt(n-1)) + floor(sqrt(n)). - Ridouane Oudra, Jun 07 2019

Example

Triangle begins:
  1,  2,  2;
  3,  4,  4,  4,  4;
  5,  6,  6,  6,  6,  6,  6;
  7,  8,  8,  8,  8,  8,  8,  8,  8;
  9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10;

Maple

A161205 := proc(n, k) if k=1 then 2*n-1; else 2*n; end if; end proc: seq(seq(A161205(n, k), k=1..2*n+1), n=1..12) ; # R. J. Mathar, Feb 16 2010

Crossrefs

Cf. A000005, A000720, A018253, A125202, A160811, A160812, A161339.

Sequence in context: A003002 A087180 A029121 * A340619 A334800 A228942

Adjacent sequences: A161202 A161203 A161204 * A161206 A161207 A161208

Keyword

easy,nonn,tabf

Author

Omar E. Pol, Jun 19 2009

Extensions

More terms from R. J. Mathar, Feb 16 2010

Status

approved