A364168 Numbers that can be written in more than one way in the form (j+2k)^2-(j+k)^2-j^2 with j,k>0.

15, 27, 32, 35, 36, 39, 51, 55, 60, 63, 64, 75, 84, 87, 91, 95, 96, 99, 100, 108, 111, 115, 119, 123, 128, 132, 135, 140, 143, 144, 147, 155, 156, 159, 160, 171, 175, 180, 183, 187, 192, 195, 196, 203, 204, 207, 215, 219, 220, 224, 228, 231, 235, 240, 243, 247, 252, 255

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Project Euler, Problem 135: Same Differences.

Example

27 is a term since (6+2*3)^2 - (6+3)^2 - 6^2 = (20+2*7)^2 - (20+7)^2 - 20^2 = 27.

Prog

(Python)
from sympy import divisors
def isok(n):
  s = 0
  for d in divisors(n):
    t = n // d + d
    if ((q:=t >> 2) << 2) == t and q < d:
      s += 1
  return s > 1
print([n for n in range(1, 256) if isok(n)])

Crossrefs

Cf. A000290, A027750, A000005.

Sequence in context: A359205 A080945 A080946 * A253056 A091236 A354714

Adjacent sequences: A364165 A364166 A364167 * A364169 A364170 A364171

Keyword

nonn

Author

Darío Clavijo, Jul 12 2023

Status

approved