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%I #8 Mar 25 2023 05:29:43
%S 3344,12636,88900,95900,109900,116900,121100,181424,271472,365552,
%T 476272,504016,975568,1016048,1354288,1375504,1407824,1552304,1628528,
%U 1641904,1862608,1882672,1902736,1909424,1929488,1962928,1982992,2003056,2009744,2029808,2049872
%N Noninfinitary weird numbers: noninfinitary abundant numbers (A348274) that are not equal to the sum of any subset of their noninfinitary divisors.
%H Amiram Eldar, <a href="/A348525/b348525.txt">Table of n, a(n) for n = 1..10000</a>
%e 3344 is a term since the sum of its noninfinitary divisors, {2, 4, 8, 22, 38, 44, 76, 88, 152, 418, 836, 1672}, is 3360 > 3344, and no subset of these divisors sums to 3344.
%t q[n_] := !IntegerQ@ Log2@ DivisorSigma[0, n]; nidiv[1] = {}; nidiv[n_] := Complement[Divisors[n], Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; s = {}; Do[If[! q[n], Continue[]]; d = nidiv[n]; If[Total[d] <= n, Continue[]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c == 0, AppendTo[s, n]], {n, 1, 13000}]; s
%Y Cf. A348271, A348274, A348341.
%Y Similar sequences: A006037, A064114, A292986, A306984, A321146, A327948.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 21 2021
%E More terms from _Amiram Eldar_, Mar 25 2023
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