%I M5372 #33 Jun 28 2017 02:25:20

%S 114,1140,18018,32130,44772,56430,67158,142310,180180,197340,241110,

%T 296010,308220,462330,591030,669900,671580,785148,815100,1004850,

%U 1077890,1080150,1156870,1177722,1222650,1281540,1475810,1511930,1571388

%N Smaller of unitary amicable pair.

%C I proved the following facts: (a) If (m,n) is a unitary amicable pair such that mod(m,4)= mod(n,4)=2 and 5 doesn't divide m*n then (10*m,10*n) is a unitary amicable pair. (b) If (m,n) is a unitary amicable pair such that m/12 and n/12 are natural numbers and gcd(m/12,12)=gcd(n/12,12)=1 then (3/2*m,3/2*n) is a unitary amicable pair. - _Farideh Firoozbakht_, Nov 27 2005

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002952/b002952.txt">Table of n, a(n) for n = 1..7896</a> (from Pedersen's website)

%H Peter Hagis, Jr., <a href="http://www.jstor.org/stable/2004356">Unitary amicable numbers</a>, Math. Comp., 25 (1971), 915-918.

%H J. M. Pedersen, <a href="http://amicable.homepage.dk/knwnunap.htm">Known Unitary Amicable Pairs</a>

%H J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Broken link]

%H J. O. M. Pedersen, <a href="http://web.archive.org/web/20140502102524/http://amicable.homepage.dk/tables.htm">Tables of Aliquot Cycles</a> [Via Internet Archive Wayback-Machine]

%H J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a> [Cached copy, pdf file only]

%H Ivars Peterson, <a href="https://www.sciencenews.org/article/amicable-pairs-divisors-and-new-record">Amicable Pairs, Divisors, and a New Record</a>, January 30 2004.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryAmicablePair.html">Unitary Amicable Number.</a>

%e (114,126) is a unitary amicable pair: 114 has unitary divisors 1, (2,57), (3,38) and (6,19), apart from 114 itself. Their sum is 126, whose unitary divisors < 126 are 1, (2,63), (7,18), (9,14) whose sum is 114.

%t uDivisors[n_] := Select[Divisors[n], # < n && GCD[#, n/#] == 1 & ]; mate[n_] := If[m = Total[uDivisors[n]]; n == Total[uDivisors[m]], m, 0]; Reap[Do[If[n < mate[n], Print[n]; Sow[n]], {n, 2, 2000000}]][[2, 1]] (* _Jean-François Alcover_, Jun 12 2012 *)

%Y Cf. A002953, A063991, A111904.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_; extended Nov 24 2005