OFFSET
1,1
COMMENTS
A number m is a term if the set {d|m ; d > 1, d < m, gcd(d, m/d) = 1} is nonempty and the harmonic mean its members is an integer.
The corresponding harmonic means are 8, 9, 15, 16, 25, 12, 21, 15, 33, 12, ...
Equivalently, numbers m such that omega(m) > 1 and (usigma(m)-m-1) | m*(2^omega(m)-2), where usigma is the sum of unitary divisors (A034448), and 2^omega(m)-2 = A034444(m)-2 = A087893 (m) is the number of the nontrivial unitary divisors of m.
The squarefree terms of A247078 are also terms of this sequence.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..150
EXAMPLE
228 is a term since the harmonic mean of its nontrivial unitary divisors, {3, 4, 12, 19, 57, 76} is 8 which is an integer.
MATHEMATICA
usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[10^6], (omega = PrimeNu[#]) > 1 && Divisible[#*(2^omega - 2), usigma[#] - # - 1] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 29 2020
STATUS
approved