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A364862 S-weird numbers: S-abundant numbers (A181487) k such that no subset of the aliquot divisors of k that are in the set S sums to k, where S is the set defined in A118372.

%I A364862 #9 Aug 12 2023 00:50:04
%S A364862 70,836,2704,2744,4030,5530,5810,5830,6230,6790,7070,7192,7210,7490,
%T A364862 7630,7910,7912,8890,9170,9272,9590,9730,10430,10570,10792,10990,
%U A364862 11410,11690,12110,12530,12670,13370,13510,13790,13930,14770,15610,15890,16030,16310,16730
%N A364862 S-weird numbers: S-abundant numbers (A181487) k such that no subset of the aliquot divisors of k that are in the set S sums to k, where S is the set defined in A118372.
%C A364862 Analogous to weird numbers (A006037) as S-perfect numbers (A118372) are analogous to perfect numbers (A000396) and S-abundant numbers (A181487) are analogous to abundant numbers (A005101).
%C A364862 Apparently, includes all the weird numbers (verified for all terms below 5*10^7). It also includes additional terms: 2704, 2744, 5530, 5810, 6230, 6790, 7070, 7210, 7490, ... .
%H A364862 Amiram Eldar, <a href="/A364862/b364862.txt">Table of n, a(n) for n = 1..10000</a>
%t A364862 weirdQ[n_, d_] := If[Total[d] <= n, False, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0];
%t A364862 S = {1}; Sweird = {}; Do[s = Total[(d = Intersection[S, Divisors[n]])]; If[s <= n, AppendTo[S, n], If[weirdQ[n, d], AppendTo[Sweird, n]]], {n, 2, 10^4}]; Sweird		
%Y A364862 Subsequence of A181487.
%Y A364862 Cf. A000396, A005101, A006037, A118372.
%K A364862 nonn
%O A364862 1,1
%A A364862 _Amiram Eldar_, Aug 11 2023