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%I #38 Mar 09 2024 05:58:50
%S 6160,12220,23500,68908,249424,425500,434784,649990,660825,1017856,
%T 1077336,1238380,1252216,1568260,1754536,2166136,2362360,2482536,
%U 2537220,2876445,3957525,4177524,4287825,5224660,5559510,5641552
%N Augmented amicable pairs (smaller member of each pair).
%C Let f(n) = 1 + sum of aliquot divisors of n; these are pairs (n,m) with f(n)=m, f(m)=n.
%C m cannot equal n. - _Harvey P. Dale_, May 18 2012
%C The term "augmented amicable numbers" was coined by Beck and Wajar (1977), who found the first 11 pairs. They also found the next 25 pairs (1993). - _Amiram Eldar_, Mar 09 2024
%H Amiram Eldar, <a href="/A007992/b007992.txt">Table of n, a(n) for n = 1..1159</a>
%H Walter E. Beck and Rudolph M. Wajar, <a href="https://www.fq.math.ca/Scanned/15-4/beck1.pdf">More reduced amicable pairs</a>, Fibonacci Quarterly, Vol. 15, No. 4 (1977), pp. 331-332.
%H Walter E. Beck and Rudolph M. Wajar, <a href="https://www.fq.math.ca/Scanned/31-4/beck.pdf">Reduced and Augmented Amicable Pairs to 10^8</a>, Fibonacci Quarterly, Vol. 31, No. 4 (1993), pp. 295-298.
%H David Moews, <a href="http://djm.cc/augmented.fmtlist">Augmented amicable pairs</a>.
%H J. O. M. Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>.
%H J. O. M. Pedersen, <a href="/A063990/a063990.pdf">Tables of Aliquot Cycles</a>. [Cached copy, pdf file only]
%H Paul Pollack, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Pollack/pollack3.html">Quasi-Amicable Numbers are Rare</a>, J. Int. Seq. 14 (2011), Article 11.5.2.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AugmentedAmicablePair.html">Augmented Amicable Pair</a>.
%t aapQ[n_]:=Module[{c=DivisorSigma[1,n]+1-n},c!=n&&DivisorSigma[ 1,c]+1-c == n]; Transpose[Union[Sort[{#,DivisorSigma[1,#]+1-#}]&/@Select[Range[ 6000000],aapQ]]] [[1]] (* _Harvey P. Dale_, May 18 2012 *)
%Y Cf. A015630.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
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