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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

%I #20 Apr 04 2023 07:43:16

%S 70,836,4030,5830,10430,10570,10990,11410,11690,12110,12530,12670,

%T 13370,13510,13790,13930,14770,15610,15890,16030,16310,16730,16870,

%U 17570,17990,18410,18830,18970,19390,19670,19810,20510,21490,21770,21910,22190,23170,23590,24290

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

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

%C Is there any number besides 836 which is in this sequence but not in A348631? - _R. J. Mathar_, Nov 16 2021

%C The next term after 836 that is not in A348631 is a(89) = 45356. - _Amiram Eldar_, Nov 21 2021

%H Amiram Eldar, <a href="/A349285/b349285.txt">Table of n, a(n) for n = 1..10000</a>

%t 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]

%Y Cf. A049603, A051378, A333928, A349284.

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 13 2021

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)