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Lesser of augmented unitary amicable pair.
2

%I #16 Mar 16 2019 15:28:08

%S 6224890,37542190,56523810,101304490,135657795,233990890,5304907426,

%T 8473747030,8483430670,9220653310,11033448910,12139959910,13108452735,

%U 13849730895,16697472870,19644687195,20321234206,23076788295,40575765615,55636542346,89094853155,101786530846

%N Lesser of augmented unitary amicable pair.

%C A pair m < n is an augmented unitary amicable pair if usigma(m) = usigma(n) = m + n - 1, where usigma(n) is the sum of unitary divisors of n (A034460).

%C The larger members are in A306873.

%H Amiram Eldar, <a href="/A306872/b306872.txt">Table of n, a(n) for n = 1..27</a> (terms below 10^12, from David Moews's site).

%H David Moews, <a href="http://djm.cc/amicable.html">Perfect, amicable and sociable numbers</a>

%H J. O. M. Pedersen, <a href="http://62.198.248.44/aliquot/tables.htm">Tables of Aliquot Cycles</a>

%e 6224890 is in the sequence since it is the lesser of the amicable pair (6224890, 7336455): usigma(6224890) = usigma(7336455) = 13561344 = 6224890 + 7336455 - 1.

%t us[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n; s={}; Do[m = us[n] + 1; If[m > n && us[m] == n - 1, AppendTo[s, n]], {n, 1, 10^9}]; s

%Y Cf. A002952, A007992, A034460, A126174, A306873.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 14 2019