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%I #35 May 21 2021 18:30:50
%S 504,2394,5544,10584,12600,21600,26880,35712,139104,133920,138240,
%T 157248,168480,224640,262080,245520,294840,311040,348192,357120,
%U 388800,399168,645624,698544,749952,756000,892800,955206,1017792,1048320
%N The sum of the two numbers in an amicable pair, A002025(n) + A002046(n).
%C This sequence initially shares many terms with A161005 because small amicable pairs are sometimes consecutive terms in the sorted list of amicable numbers, A063990.
%C This sequence is sorted by the smaller (abundant) member from A002025, so a(n) is not increasing. - _Jeppe Stig Nielsen_, Jan 27 2015
%C Duplicates occur, e.g., a(32)=a(35)=1296000. - _Jeppe Stig Nielsen_, Jan 27 2015
%C Comment originally by _M. F. Hasler_, Dec 14 2013, in A161005: "Also: The common value of sigma(a) = sigma(b) of the amicable pairs (a,b). See A137231 for the analog for amicable triples, and A116148 for quadruples." - _Jeppe Stig Nielsen_, Jan 27 2015
%C It is not known if a(n) is always even (see Hagis links). - _Jeppe Stig Nielsen_, Jan 31 2015
%C Are all terms abundant (A005101)? The first 10000 terms are. - _Ivan N. Ianakiev_, Apr 15 2021
%H Amiram Eldar, <a href="/A180164/b180164.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H Peter Hagis, <a href="http://dx.doi.org/10.1090/S0025-5718-1970-0276167-4">Lower bounds for relatively prime amicable numbers of opposite parity</a>, Math. Comp. 24 (1970), 963-968.
%H Peter Hagis, <a href="http://www.jstor.org/stable/2688105">Relatively Prime Amicable Numbers of Opposite Parity</a>, Mathematics Magazine, Vol. 43, No. 1 (Jan., 1970), pp. 14-20.
%H Eric W. Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairSum.html">Pair Sum</a>.
%F a(n) = A259180(2n-1) + A259180(2n). - _Omar E. Pol_, Oct 22 2017
%e a(9) = A002025(9) + A002046(9) = 63020 + 76084 = 139104.
%t s[n_] := DivisorSigma[1,n]-n; smallAmicableQ[n_] := Module[{b=s[n]}, n<b && s[b]==n]; a=Select[Range[10^6], smallAmicableQ]; Table[n+s[n],{n,a}]
%Y Cf. A002025, A002046, A066539, A259180 (amicable pairs).
%K nonn
%O 1,1
%A _T. D. Noe_, Aug 14 2010
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