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.

70, 836, 2704, 2744, 4030, 5530, 5810, 5830, 6230, 6790, 7070, 7192, 7210, 7490, 7630, 7910, 7912, 8890, 9170, 9272, 9590, 9730, 10430, 10570, 10792, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730

Offset: 1

Author

Amiram Eldar, Aug 11 2023

Keywords

• nonn

Comments

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).

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, ... .

Links

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

Crossrefs

Subsequence of A181487.

Cf. A000396, A005101, A006037, A118372.

Programs

Mathematica

weirdQ[n_, d_] := If[Total[d] <= n, False, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0];
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