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

1,1

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

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		

Crossrefs

Subsequence of A181487.

Cf. A000396, A005101, A006037, A118372.

Sequence in context: A212236 A177298 A230897 * A006037 A002975 A354282

Adjacent sequences: A364859 A364860 A364861 * A364863 A364864 A364865

Keyword

nonn

Author

Amiram Eldar, Aug 11 2023

Status

approved