|
%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
|
