A349285 (1+e)-weird numbers: (1+e)-abundant numbers k such that no subset of the aliquot (1+e)-divisors of k sums to k.

70, 836, 4030, 5830, 10430, 10570, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17570, 17990, 18410, 18830, 18970, 19390, 19670, 19810, 20510, 21490, 21770, 21910, 22190, 23170, 23590, 24290

Offset: 1

Author

Amiram Eldar, Nov 13 2021

Keywords

• nonn

Comments

The (1+e)-abundant numbers are numbers k such that A051378(k) > 2*k (union of A333928 and A349284).

Is there any number besides 836 which is in this sequence but not in A348631? - R. J. Mathar, Nov 16 2021

The next term after 836 that is not in A348631 is a(89) = 45356. - Amiram Eldar, Nov 21 2021

Links

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

Crossrefs

Cf. A049603, A051378, A333928, A349284.

Similar sequences: A006037, A064114, A292986, A306984, A321146, A327948, A348525.

Programs

Mathematica

divQ[n_, m_] := (n > 0 && (m == 0 || Divisible[n, m])); oeDivQ[n_, d_] := Module[{f = FactorInteger[n]}, And @@ MapThread[divQ, {f[[;; , 2]], IntegerExponent[d, f[[;; , 1]]]}]]; oeDivs[1] = {1}; oeDivs[n_] := Module[{d = Divisors[n]}, Select[d, oeDivQ[n, #] &]]; oesigma[1] = 1; oesigma[n_] := Total@oeDivs[n]; oeAbundantQ[n_] := oesigma[n] > 2*n; oeWeirdQ[n_] := oeAbundantQ[n] && Module[{d = Most[oeDivs[n]]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; Select[Range[12000], oeWeirdQ]