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

1,1

Links

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

Example

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.

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

Crossrefs

Cf. A348271, A348274, A348341.

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

Sequence in context: A270338 A054356 A358312 * A255731 A204884 A204880

Adjacent sequences: A348522 A348523 A348524 * A348526 A348527 A348528

Keyword

nonn

Author

Amiram Eldar, Oct 21 2021

Extensions

More terms from Amiram Eldar, Mar 25 2023

Status

approved