A180330 Smallest amicable number of the form 2^n * p * q for which the larger member of the amicable pair has the same form, where p and q are distinct odd primes.

2620, 10744, 66928, 2082464, 7677248, 1750776704, 749380864, 7074650624, 25937232896, 161899964416, 3949032574976, 56691934109696, 162222327218176, 5469697508737024, 21547979005558784, 48336727662002176, 2961911925308653568, 5591728346540539904

Offset

2,1

Comments

That is, the amicable pair is (2^n pq, 2^n rs) for odd primes p, q, r, s. See A180331 for the numbers 2^n rs. It is easy to show that the four primes must satisfy the equation (p+1)(q+1) = (r+1)(s+1). These amicable pairs are a subset of the regular type (2,2) pairs, which are cataloged by Pedersen. These amicable pairs can be found by using Herman te Riele's method 2. Amicable pairs of this form are known for 1 < n < 49. Do they exist for all n?

Links

Table of n, a(n) for n=2..19.

Sergei Chernykh, Amicable numbers list.

Jan Munch Pedersen, Regular type (2,2) amicable pairs.

Herman J. J. te Riele, On generating new amicable pairs from given amicable pairs, Math. Comp. 42 (1984), 219-223.

Crossrefs

Cf. A002025, A063990, A180331.

Sequence in context: A066871 A180650 A245008 * A238921 A156398 A139675

Adjacent sequences: A180327 A180328 A180329 * A180331 A180332 A180333

Keyword

nonn

Author

T. D. Noe, Sep 07 2010

Extensions

a(18)-a(19) from Chernykh's database added by Amiram Eldar, Jul 26 2025

Status

approved