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
Amiram Eldar, Table of n, a(n) for n = 1..10000
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