A259225 Smallest oblong number greater than or equal to n.

0, 2, 2, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72

Offset: 0

Author

Michel Marcus, Jun 21 2015

Keywords

• nonn

Links

• Casey Douglas, The Next Square or Pronic, June 2012. [Wayback Machine copy]

Crossrefs

Cf. A002378 (oblong numbers), A048761 (similar, with square instead).

Programs

Mathematica

f[n_] := n*(n + 1); g[n_] := (Sqrt[4*n + 1] - 1)/2; a[n_] := f[Ceiling[g[n]]]; Array[a, 100, 0] (* Amiram Eldar, Aug 16 2022 *)

PARI

a(n) = my(k = 0); while(k*(k+1)
				

Formula

Sum_{n>=1} 1/a(n)^2 = 4 - Pi^2/3. - Amiram Eldar, Aug 16 2022