OFFSET
1,1
COMMENTS
Original name: Numbers k such that A211996(k) is not zero
For any n, the equation x^4 + a(n)*y^4 = z^2 is solvable in integers. - Arkadiusz Wesolowski, Aug 15 2013
The asymptotic density of this sequence is 0 (De Koninck et al., 2024). - Amiram Eldar, Nov 05 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
David Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. Vol. 34 (2), (1991), pp. 181-185.
Jean-Marie De Koninck, A. Arthur Bonkli Razafindrasoanaivolala, and Hans Schmidt Ramiliarimanana, Integers with a sum of co-divisors yielding a square, Research in Number Theory, Vol. 10, No. 2 (2024), Article 30; author's copy.
MATHEMATICA
q[k_] := DivisorSum[k, 1 &, #^2 <= k && IntegerQ[Sqrt[# + k/#]] &] > 0; Select[Range[300], q] (* Amiram Eldar, Nov 05 2024 *)
PROG
(PARI) is(k) = k > 1 && fordiv(k, d, if(issquare(d + k/d), return(1)); if(d^2 > k, return(0))); \\ Amiram Eldar, Nov 05 2024
(Python)
from itertools import count, islice
from sympy import divisors
from sympy.ntheory.primetest import is_square
def A218381_gen(startvalue=1): # generator of terms >= startvalue
for k in count(max(startvalue, 1)):
for d in divisors(k):
if d**2>k:
break
if is_square(k//d+d):
yield k
break
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 27 2012
EXTENSIONS
Simpler name from M. F. Hasler, Jun 18 2026
STATUS
approved
