A306875 Lesser of reduced unitary amicable pair.

172622505, 6217560734, 16017860054, 18102483014, 20021589510, 31285993970, 32576024810, 39270110990, 68700877014, 80170395410, 81142298930, 99542647490, 125182657005, 144194617490, 153113328654, 181335043274, 318710758730, 374642686418, 378482712530, 455440763414

Offset

1,1

Comments

A pair m < n is a reduced 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 A306876.

Links

Amiram Eldar, Table of n, a(n) for n = 1..28 (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

172622505 is in the sequence since it is the lesser of the amicable pair (172622505, 175742294): usigma(172622505) = usigma(175742294) = 348364800 = 172622505 + 175742294 + 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. A003502, A002952, A126172, A034460, A306876.

Sequence in context: A104331 A233598 A187316 * A251999 A003850 A003843

Adjacent sequences: A306872 A306873 A306874 * A306876 A306877 A306878

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved