A066784 Numbers n such that (n, sigma(n)) lies on the hyperbola y^2 - x^2 = m^2, for some natural number m, i.e., sigma(n)^2 - n^2 = m^2.

1, 90, 392448, 411264, 804384, 871416, 1284192, 1935360, 7456512, 396168192, 24193572480, 43171285248, 54585498240, 63178786944, 123570274464, 730078562304, 823442861592, 1420069242240, 2354025332736, 2506251331584, 3606011136000, 3697798293504, 9951618862080

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Example

sigma(90)^2 - 90^2 = 234^2 - 90^2 = 216^2, so 90 is a term of the sequence.

Mathematica

Select[ Range[ 1, 10^6 ], IntegerQ[ Sqrt[ DivisorSigma[ 1, # ]^2 - #^2 ] ] & ]

Crossrefs

Cf. A066764.

Sequence in context: A172572 A052277 A172671 * A135321 A135428 A028672

Adjacent sequences: A066781 A066782 A066783 * A066785 A066786 A066787

Keyword

nonn

Author

Joseph L. Pe, Jan 18 2002

Extensions

a(7)-a(10) from Sean A. Irvine, Nov 06 2023

a(11)-a(23) from Martin Ehrenstein, Jul 12 2024

Status

approved