A377134 Abundant numbers k such that k^2 + A033880(k)^2 is a perfect square.

336, 1080, 3078, 6048, 6552, 19845, 47616, 239760, 435708, 599400, 760320, 873180, 997920, 1468800, 1602300, 2004480, 4312440, 4612608, 4713984, 10181808, 10665984, 11554816, 12160512, 24149664, 31244850, 46431744, 56439504, 64995840, 116958492

Offset

1,1

Comments

These abundant numbers along with their abundances form the legs of an integral Pythagorean triangle.

Odd terms are very rare: 19845 is the only one up to 10^9.

Links

Table of n, a(n) for n=1..29.

Example

336 is a term because its abundance is 320 and 320^2 + 336^2 = 464^2.

Mathematica

l={}; Do[a=DivisorSigma[1, n]-2*n; If[a>0&&IntegerQ@Sqrt[n^2+a^2], AppendTo[l, n]], {n, 12, 2*10^8}]; l

Prog

(PARI) for(n=12, 2*10^8, a=sigma(n)-2*n; a>0&&issquare(n^2+a^2)&&print1(n", "))
(Python)
import sympy as sp
for i in range(12, 200000000):
    a=sp.ntheory.factor_.divisor_sigma(i) - 2*i
    if a>0 and sp.ntheory.primetest.is_square(i*i+a*a):
        print(i, end=", ")

Crossrefs

Cf. A005101, A033880, A000290.

Sequence in context: A181256 A006909 A067708 * A059467 A348343 A237862

Adjacent sequences: A377131 A377132 A377133 * A377135 A377136 A377137

Keyword

nonn

Author

Waldemar Puszkarz, Oct 17 2024

Status

approved