A180335 Number of amicable pairs of the form (2^n * pq, 2^n * rs), where p, q, r, and s are distinct odd primes.

0, 2, 1, 7, 3, 3, 2, 7, 1, 8, 4, 8, 7, 5, 6, 15, 4, 9, 9, 14, 8, 15, 8, 15

Offset

1,2

Comments

There are only a finite number of such pairs for each n. A180330(n) is the smallest value of 2^n * pq which is part of an amicable pair. The terms in this sequence equal the count of such amicable pairs in Pedersen's table up to n=22, after which the table stops being a complete list of all amicable pairs of the form 2^n * pq. Currently, Pedersen's table lists 4 such amicable pairs for n=23 when there are actually 8 pairs.

Links

Table of n, a(n) for n=1..24.

J. M. Pedersen, Regular type (2,2) amicable pairs

Example

Eight pairs for n=23, with new ones indicated by *:
(112072375885373577887744, 112072384861110016147456) *
(1268674663237438821892096, 1268674685089131637243904)
(207428765646084356836425728, 207428778650058836339064832) *
(3201546606177940316018966528, 3201546948253280471426793472)
(3246126368411500102994100224, 3246126753752370852634034176)
(30886958374694867104144818176, 30886959839775761339382759424) *
(58230121837690366602703273984, 58230128772645945195748130816)
(1564092755993481057609717907456, 1564092823984266648474085228544) *

Crossrefs

Cf. A180650, A180651 (the amicable pairs for each n)

Sequence in context: A090699 A214550 A120903 * A257699 A160535 A258235

Adjacent sequences: A180332 A180333 A180334 * A180336 A180337 A180338

Keyword

hard,nonn

Author

T. D. Noe, Sep 25 2010

Status

approved