A306873 Larger of augmented unitary amicable pair.

7336455, 41337555, 110691295, 108212055, 154646206, 313439511, 6400149855, 9971007915, 10049576691, 9849706755, 12125842995, 12180547995, 14064001666, 18225635506, 26623431835, 20500208806, 23746912995, 23952459706, 43137954706, 56039259255, 99517314526, 125782774755

Offset

1,1

Comments

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).

The terms are ordered according to their lesser counterparts (A306872).

Links

Amiram Eldar, Table of n, a(n) for n = 1..27 (terms with lesser member below 10^12, from David Moews's site).

David Moews, Perfect, amicable and sociable numbers

J. O. M. Pedersen, Tables of Aliquot Cycles

Example

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

Mathematica

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

Crossrefs

Cf. A002953, A015630, A034460, A126175, A306872.

Sequence in context: A116236 A116259 A158256 * A269220 A268406 A302135

Adjacent sequences: A306870 A306871 A306872 * A306874 A306875 A306876

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved