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A064114
Unitary weird numbers: unitary abundant (A034683) but not unitary pseudoperfect (A293188).
16
70, 4030, 5390, 5830, 10430, 10570, 10990, 11410, 11690, 11830, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17010, 17570, 17990, 18410, 18830, 18970, 19390, 19670, 19810, 20230, 20510, 21490, 21770, 21910
OFFSET
1,1
COMMENTS
Terms that are not (regular) weird (A006037): 5390, 11830, 17010, 20230, 25270, 37030, 51030, 58870, 67270, 93170, 95830, ... - Amiram Eldar, Dec 01 2018
Conjecture: All the terms are divisible by 10 (tested on the first 10^6 terms). - Amiram Eldar, Oct 19 2019
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are , 0, 1, 1, 4, 205, 1680, 14302, 165369, 1682383, 16326260, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0016... . - Amiram Eldar, Jan 24 2023
LINKS
EXAMPLE
70 is in the sequence since the sum of its proper unitary divisors, 1, 2, 5, 7, 10, 14, 35 is 74 > 70, yet no subset of these divisors has the sum 74.
MATHEMATICA
udiv[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; weirdQ[n_] := Module[{d = Most[udiv[n]]}, If[Total[d] < n, False, c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; c == 0]]; Select[Range[100000], weirdQ] (* Amiram Eldar, Dec 01 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Sep 08 2001
EXTENSIONS
a(25)-a(38) from Amiram Eldar, Dec 01 2018
STATUS
approved