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Triangle read by rows in which row n lists 2n-1 followed by 2n numbers 2n.
15

%I #17 Jun 07 2019 20:32:01

%S 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,

%T 10,10,10,10,11,12,12,12,12,12,12,12,12,12,12,12,12,13,14,14,14,14,14,

%U 14,14,14,14,14,14,14,14,14,15,16,16,16,16,16,16,16,16

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

%C Row sums: A125202(n+1). - _R. J. Mathar_, Feb 16 2010

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polprdipi.jpg">Illustration: Divisors and pi(x)</a>

%F 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

%F a(n) = A000196(n-1) + A000196(n) = floor(sqrt(n-1)) + floor(sqrt(n)). - _Ridouane Oudra_, Jun 07 2019

%e Triangle begins:

%e 1, 2, 2;

%e 3, 4, 4, 4, 4;

%e 5, 6, 6, 6, 6, 6, 6;

%e 7, 8, 8, 8, 8, 8, 8, 8, 8;

%e 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10;

%p 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

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

%K easy,nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jun 19 2009

%E More terms from _R. J. Mathar_, Feb 16 2010