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%I #22 Jan 24 2023 02:51:06
%S 70,4030,5390,5830,10430,10570,10990,11410,11690,11830,12110,12530,
%T 12670,13370,13510,13790,13930,14770,15610,15890,16030,16310,16730,
%U 16870,17010,17570,17990,18410,18830,18970,19390,19670,19810,20230,20510,21490,21770,21910
%N Unitary weird numbers: unitary abundant (A034683) but not unitary pseudoperfect (A293188).
%C Terms that are not (regular) weird (A006037): 5390, 11830, 17010, 20230, 25270, 37030, 51030, 58870, 67270, 93170, 95830, ... - _Amiram Eldar_, Dec 01 2018
%C Conjecture: All the terms are divisible by 10 (tested on the first 10^6 terms). - _Amiram Eldar_, Oct 19 2019
%C 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
%H Amiram Eldar, <a href="/A064114/b064114.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%Y Cf. A006037, A034683, A293188.
%K nonn
%O 1,1
%A _Naohiro Nomoto_, Sep 08 2001
%E a(25)-a(38) from _Amiram Eldar_, Dec 01 2018
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