OFFSET
1,1
COMMENTS
Let f(n) = 1 + sum of aliquot divisors of n; these are pairs (n,m) with f(n)=m, f(m)=n.
m cannot equal n. - Harvey P. Dale, May 18 2012
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1159
Walter E. Beck and Rudolph M. Wajar, More reduced amicable pairs, Fibonacci Quarterly, Vol. 15, No. 4 (1977), pp. 331-332.
Walter E. Beck and Rudolph M. Wajar, Reduced and Augmented Amicable Pairs to 10^8, Fibonacci Quarterly, Vol. 31, No. 4 (1993), pp. 295-298.
David Moews, Augmented amicable pairs.
J. O. M. Pedersen, Tables of Aliquot Cycles.
J. O. M. Pedersen, Tables of Aliquot Cycles. [Cached copy, pdf file only]
Paul Pollack, Quasi-Amicable Numbers are Rare, J. Int. Seq. 14 (2011), Article 11.5.2.
Eric Weisstein's World of Mathematics, Augmented Amicable Pair.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,nice,changed
AUTHOR
STATUS
approved