A337988 Numbers that are the sum of the squares of two of their distinct divisors.

20, 80, 90, 180, 272, 320, 360, 468, 500, 650, 720, 810, 980, 1088, 1280, 1332, 1440, 1620, 1872, 2000, 2250, 2420, 2448, 2450, 2600, 2880, 2900, 3240, 3380, 3600, 3920, 4160, 4212, 4352, 4410, 4500, 5120, 5328, 5760, 5780, 5850, 6480, 6642, 6800, 7220, 7290, 7488, 7650

Offset: 1

Author

Wesley Ivan Hurt, Oct 06 2020

Keywords

• nonn

Examples

			20 = 2^2 + 4^2, so 20 is in the sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000404.

Programs

Mathematica

Select[Range[10^4], 1 == Catch@ Do[Do[If[#2[[i]]^2 + #2[[j]]^2 == #1, Throw[1]], {j, i + 1, #3}], {i, #3}] & @@ {#, Divisors[#], DivisorSigma[0, #]} &] (* Michael De Vlieger, Oct 10 2020 *)

PARI

isok(m) = {my(d=divisors(m)); for (i=2, #d, for (j=1, i-1, if (d[i]^2+d[j]^2 == m, return (1));););} \\ Michel Marcus, Oct 07 2020

Python

from sympy import divisors, integer_nthroot
A337988_list = []
for n in range(1,10**6):
    for d in divisors(n):
        if 2*d*d >= n:
            break
        a, b = integer_nthroot(n-d*d,2)
        if b and n % a == 0:
            A337988_list.append(n)
            break # Chai Wah Wu, Oct 30 2020

Extensions

More terms from Michel Marcus, Oct 07 2020