Search: id:A002952
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%I A002952 M5372
%S A002952 114,1140,18018,32130,44772,56430,67158,142310,180180,197340,241110,296010,
%T A002952 308220,462330,591030,669900,671580,785148,815100,1004850,1077890,
%U A002952 1080150,1156870,1177722,1222650,1281540,1475810,1511930,1571388
%N A002952 Smaller of unitary amicable pair.
%C A002952 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 (mymontain(AT)yahoo.com), Nov 27 2005
%D A002952 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002952 P. Hagis, Jr., Unitary amicable numbers, Math. Comp., 25 (1971), 915-918.
%H A002952 J. M. Pedersen, <a href="http://amicable.homepage.dk/knwnunap.htm">Known 
               Unitary Amicable Pairs</a>
%H A002952 I. Peterson, <a href="http://www.sciencenews.org/20040131/mathtrek.asp">
               Math Trek</a>
%H A002952 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               UnitaryAmicablePair.html">Link to a section of The World of Mathematics.</
               a>
%H A002952 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables 
               of Aliquot Cycles</a>
%e A002952 (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.
%Y A002952 Cf. A002953, A063991, A111904.
%Y A002952 Sequence in context: A043403 A122279 A126169 this_sequence A108344 A162675 
               A112485
%Y A002952 Adjacent sequences: A002949 A002950 A002951 this_sequence A002953 A002954 
               A002955
%K A002952 nonn,nice
%O A002952 1,1
%A A002952 N. J. A. Sloane (njas(AT)research.att.com); extended Nov 24 2005

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