A259227 Hydropronic numbers: numbers n that can be written as a product of 2 integers whose sum is equal to ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)).

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 66, 70, 72, 77, 80, 81, 84, 88, 90, 91, 96, 99, 100, 104, 108, 110, 112, 117, 120, 121, 126, 130, 132, 135, 140, 143, 144, 150, 154, 156, 160

Offset: 1

Author

Michel Marcus, Jun 21 2015

Keywords

• nonn

Comments

It appears that ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(n)) is A027434(n).

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Casey Douglas, The Next Square or Pronic, June 2012.
• Casey Douglas, Hydropronic Sequence?, June 2012.
• Casey Douglas, Another Quickie, July 2012.

Programs

Mathematica

Select[Range@160, IntegerQ@Sqrt[((r = Ceiling@Sqrt@#) + Ceiling[#/r])^2 - 4 #] &] (* Ivan Neretin, Oct 16 2016 *)

PARI

isok(n) = {d = divisors(n); for (k=1, #d, if ((d[k] + n/d[k]) == ceil(n/ceil(sqrt(n)))+ceil(sqrt(n)), return (1)););}