A322688 Two-column table read by rows: Primitive distinct pairs that have the same value of phi, sigma, and tau.

568, 638, 1824, 1836, 3051, 3219, 4185, 4389, 4960, 5236, 6368, 6764, 7749, 8151, 9184, 9724, 9760, 11050, 11032, 12470, 11176, 12586, 13420, 14350, 15169, 15265, 17376, 19206, 18788, 20150, 23848, 26866, 26355, 27962, 26784, 29260, 28809, 30381, 30199, 30217, 32128, 33128, 32940, 37050, 34144, 36244, 37592, 39795

Offset

1,1

Comments

The terms are consecutive pairs, ordered so that (A) a(2i-1) < a(2i) for i > 0, and (B) a(2i+1) < a(2i+3) for i >= 0. This sequence has primitive solutions only. If k is relatively prime to all of the terms in a primitive pair, then multiplying the terms in that pair by k gives another solution - see A134922. In Burton's book (see references), problem 3 in section 7.2 asks the reader to prove a special case for (568,638).

References

David Burton, Elementary Number Theory, 4th edition, 1998, section 7.2.

Links

Jud McCranie, Table of n, a(n) for n = 1..10000

Example

phi(568)=phi(638)=280; sigma(568)=sigma(638)=1080; tau(568)=tau(638)=8.

Crossrefs

Cf. A134922, A322687, A322689, A322690, A322691, A322692, A322693, A322694, A322695, A322696, A322696.

Sequence in context: A233057 A087424 A134922 * A234233 A234228 A184682

Adjacent sequences: A322685 A322686 A322687 * A322689 A322690 A322691

Keyword

nonn,tabf

Author

Jud McCranie, Dec 31 2018

Status

approved