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A335269
Numbers for which the harmonic mean of the nontrivial unitary divisors is an integer.
3
228, 345, 1645, 2120, 4025, 4386, 4977, 7725, 8041, 13026, 23881, 24157, 24336, 51925, 88473, 115957, 150161, 169893, 229177, 255041, 278721, 322592, 342637, 377201, 490725, 538625, 656937, 1497517, 1566981, 2132021, 3256261, 3847001, 4646101, 5054221, 5524897
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
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
The unitary version of A247078.
Sequence in context: A252451 A305063 A258550 * A252228 A252221 A154519
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 29 2020
STATUS
approved