A306872 Lesser of augmented unitary amicable pair.

6224890, 37542190, 56523810, 101304490, 135657795, 233990890, 5304907426, 8473747030, 8483430670, 9220653310, 11033448910, 12139959910, 13108452735, 13849730895, 16697472870, 19644687195, 20321234206, 23076788295, 40575765615, 55636542346, 89094853155, 101786530846

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 larger members are in A306873.

Links

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

David Moews, Perfect, amicable and sociable numbers

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

Example

6224890 is in the sequence since it is the lesser 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, n]], {n, 1, 10^9}]; s

Crossrefs

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

Sequence in context: A254360 A224640 A185887 * A186838 A204654 A138941

Adjacent sequences: A306869 A306870 A306871 * A306873 A306874 A306875

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved