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 A265726 Primitive weird numbers whose abundance is a record. 2

%I

%S 70,836,7192,9272,73616,243892,338572,1188256,1901728,3963968,

%T 28279232,36228736,91322752,141659096,263144192,351295232,664373504,

%U 2113834496,5522263024,6933503488,19179527168,22755515392,31574500724,98620009472,135895635968

%N Primitive weird numbers whose abundance is a record.

%C Although the abundance A(n) = sigma(n) - 2n is increasing, the (relative) abundancy sigma(n)/n is decreasing, except at indices {3, 6, 8, 15, 16, 19, 24 ...}. No term has larger abundancy than 2 + 2/35, that of a(1). - _M. F. Hasler_, Nov 14 2018

%H Douglas E. Iannucci, <a href="http://arxiv.org/abs/1504.02761">On primitive weird numbers of the form 2^k*p*q</a>, arXiv:1504.02761 [math.NT], 2015.

%H Giuseppe Melfi, <a href="http://dx.doi.org/10.1016/j.jnt.2014.07.024"> On the conditional infiniteness of primitive weird numbers</a>, Journal of Number Theory, Vol. 147, Feb 2015, pgs 508-514.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Weird_number"> Weird number</a>

%e a(1) = 70 since it is the first term in A002975; its abundance is 4.

%e a(2) is 836 since its abundance, 8, exceeds that of a(1); 4.

%e a(3) is 7192 = A002975(5) since its abundance, 16, exceeds that of a(2) and that of A002975(1..4).

%t (* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := DivisorSigma[1, n] - 2n; k = 1; lsu = {}; mx = 0; While[k < 647, ds = f@ lst[[k]]; If[ds > mx, mx = ds; AppendTo[lsu, lst[[k]]]]; k++]; lsu

%Y Cf. A002975, A258250, A258333, A258374, A258375, A258401, A258882, A258883, A258884, A258885, A265727, A265728.

%K nonn

%O 1,1

%A Douglas E. Iannucci and _Robert G. Wilson v_, Dec 14 2015

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)