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

Author

Jud McCranie, Dec 31 2018

Keywords

• nonn
• tabf

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).

Examples

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

References

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

Links

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

Crossrefs

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