A395626 Numbers x*y such that |x-y| is a square, with nonnegative integers x and y.

0, 1, 2, 4, 5, 6, 9, 10, 12, 16, 17, 20, 21, 22, 25, 26, 30, 32, 36, 37, 42, 45, 49, 50, 52, 54, 56, 57, 60, 64, 65, 70, 72, 76, 77, 80, 81, 82, 84, 90, 96, 100, 101, 102, 105, 110, 112, 116, 117, 121, 122, 132, 136, 140, 144, 145, 150, 156, 160, 161, 162, 165, 166

Offset

1,3

Comments

Contains A000290 (the squares) and A000290 + 1.

Links

Žiga Pirc, Table of n, a(n) for n = 1..10000

Prog

(PARI) select( {is_A395626(n)=fordiv(n+=!n, d, d*d>n&&break; issquare(n/d-d)&&return(1))}, [0..166])
(Python)
from itertools import count, islice
from sympy import divisors
from sympy.ntheory.primetest import is_square
def A395626_gen(startvalue=0): # generator of terms >= startvalue
    for k in count(max(startvalue, 0)):
        if k == 0:
            yield k
        else:
            for d in divisors(k):
                if d**2>k:
                    break
                if is_square(k//d-d):
                    yield k
                    break
A395626_list = list(islice(A395626_gen(), 30)) # Chai Wah Wu, Jun 24 2026

Crossrefs

Cf. A000290, A218381 (same with + instead of -), A394904 (union of this and A218381), A397224.

Sequence in context: A352508 A125297 A194469 * A143072 A089648 A062861

Adjacent sequences: A395623 A395624 A395625 * A395627 A395628 A395629

Keyword

nonn,easy,new

Author

M. F. Hasler, Jun 18 2026

Status

approved