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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..151

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]

CROSSREFS

Cf. A049603, A051378, A333928, A349284.

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

Sequence in context: A354282 A329190 A258250 * A335008 A258882 A265726

Adjacent sequences:  A349282 A349283 A349284 * A349286 A349287 A349288

KEYWORD

nonn

AUTHOR

Amiram Eldar, Nov 13 2021

STATUS

approved

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Last modified May 27 01:53 EDT 2022. Contains 354092 sequences. (Running on oeis4.)