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A363052
Integers m for which there exist positive integers j, k such that j*k*(j+k) = m^2.
0
4, 18, 24, 32, 36, 50, 60, 108, 140, 144, 150, 192, 252, 256, 288, 300, 360, 392, 400, 480, 486, 500, 540, 588, 648, 780, 816, 864, 882, 900, 972, 1008, 1014, 1050, 1120, 1152, 1156, 1176, 1200, 1350, 1372, 1452, 1536, 1620, 1764, 1800, 1848, 2016, 2040, 2048, 2178
OFFSET
1,1
COMMENTS
All terms are even.
EXAMPLE
24 is a term: j*k*(j+k) = 24^2 for j=2, k=16.
MATHEMATICA
Select[2*Range@500,
Length@Select[Table[(Sqrt[b^2 + 4 #^2/b] - b)/2, {b, #}], IntegerQ] >
0 &]
Select[Union@
Flatten@Table[Sqrt[a*b (a + b)], {a, 1, 80}, {b, a, 500}],
IntegerQ[#] && # < 1000 &]
PROG
(Python)
from itertools import count, islice
from sympy import integer_nthroot, divisors
def A363052_gen(startvalue=1): # generator of terms >= startvalue
for m in count(max(startvalue, 1)):
for k in divisors(m**2, generator=True):
p, q = integer_nthroot(k**4+(k*m**2<<2), 2)
if q:
a, b = divmod(p-k**2, k<<1)
if a > 0 and not b:
yield m
break
A363052_list = list(islice(A363052_gen(), 20)) # Chai Wah Wu, Jul 03 2023
CROSSREFS
Cf. A088915.
Sequence in context: A022384 A093022 A255409 * A057342 A192195 A099565
KEYWORD
nonn,easy
AUTHOR
Zhining Yang, May 15 2023
STATUS
approved