A322688 - OEIS

%I #23 Jan 15 2019 17:27:13

%S 568,638,1824,1836,3051,3219,4185,4389,4960,5236,6368,6764,7749,8151,

%T 9184,9724,9760,11050,11032,12470,11176,12586,13420,14350,15169,15265,

%U 17376,19206,18788,20150,23848,26866,26355,27962,26784,29260,28809,30381,30199,30217,32128,33128,32940,37050,34144,36244,37592,39795

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

%C 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).

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

%H Jud McCranie, <a href="/A322688/b322688.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%K nonn,tabf

%O 1,1

%A _Jud McCranie_, Dec 31 2018