A007992 Augmented amicable pairs (smaller member of each pair).

6160, 12220, 23500, 68908, 249424, 425500, 434784, 649990, 660825, 1017856, 1077336, 1238380, 1252216, 1568260, 1754536, 2166136, 2362360, 2482536, 2537220, 2876445, 3957525, 4177524, 4287825, 5224660, 5559510, 5641552

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Cf. A015630.

Programs

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 *)