A348525 Noninfinitary weird numbers: noninfinitary abundant numbers (A348274) that are not equal to the sum of any subset of their noninfinitary divisors.

3344, 12636, 88900, 95900, 109900, 116900, 121100, 181424, 271472, 365552, 476272, 504016, 975568, 1016048, 1354288, 1375504, 1407824, 1552304, 1628528, 1641904, 1862608, 1882672, 1902736, 1909424, 1929488, 1962928, 1982992, 2003056, 2009744, 2029808, 2049872

Offset: 1

Author

Amiram Eldar, Oct 21 2021

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A348271, A348274, A348341.

Similar sequences: A006037, A064114, A292986, A306984, A321146, A327948.

Programs

Mathematica

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

Extensions

More terms from Amiram Eldar, Mar 25 2023