The first few
for which Euler's rule is satisfied are ,,,,,
... (OEIS A094445 and A094446),
with no others for , corresponding to the
triples , (23, 47, 1151), (191, 383, 73727),
..., giving the amicable pairs (220, 284), (17296,
18416), (9363584, 9437056), ....
Borho, W. "On Thabit ibn Kurrah's Formula for Amicable Numbers." Math. Comput.26, 571-578, 1972.Dickson,
L. E. History
of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York:
Dover, 2005.Euler, L. "De Numeris Amicabilibus." In Opera
Omnia, Series Prima, Vol. 2. Leipzig, Germany: Teubner, pp. 63-162,
1915.Sloane, N. J. A. Sequences A094445
and A094446 in "The On-Line Encyclopedia
of Integer Sequences."te Riele, H. J. J. "Four Large
Amicable Pairs." Math. Comput.28, 309-312, 1974.
and 
are an amicable pair if
the three integers
and 
satisfying 
(Dickson 2005, p. 42). However, there are
many amicable pairs which do not satisfy Euler's
rule, so it is a sufficient but not necessary condition for amicability. Euler's rule is a generalization
of Thābit ibn Qurra rule.
for which Euler's rule is satisfied are 
, 
, 
, 
, 
,
... (OEIS A094445 and A094446),
with no others for 
, corresponding to the
triples 
, (23, 47, 1151), (191, 383, 73727),
..., giving the amicable pairs (220, 284), (17296,
18416), (9363584, 9437056), ....
