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%I #12 Feb 28 2016 08:09:51
%S 70,232374697216,73616,9272,243892,343876,4128448,519712,1901728,
%T 338572,5568448,6621632,272240768,4960448,7470272,1673087984,
%U 146279296,5440192,91322752,8134208,35442304,286717696,54962343424,110232704,6460864,2812606976,44473216,141659096,33736064,58668928,9537494528,37499776,292335872,795730688,530110208,18657360896,16995175424,664373504,266311424,23049995264,15152370176,17124699136,64015565312,52059008
%N Least primitive weird number, pwn, (A002975) whose abundance is divisible by the n-th prime (A000040), or 0 if no such pwn exists.
%C No odd weird number exists below 10^21. The search is done on the volunteer computing project yoyo@home. - _Wenjie Fang_, Feb 23 2014
%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 Linked In, <a href="https://www.linkedin.com/grp/post/4510047-5820529955682926595">Number Theory, A very big weird number</a>
%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, pp. 508-514.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Weird_number">Weird number</a>
%e a(1) = 70 since it is the least pwn whose abundance, 4, is divisible by the first prime, 2.
%e a(2) = 0 since there is no known odd pwn and if there were, there is no reason why the abundance would be == 0 (mod 3).
%e a(3) = 73616 since it is the first pwn whose abundance, 80, is divisible by the third prime, 5.
%t (* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := Select[lst, Mod[ DivisorSigma[1, #] - 2#, Prime@ n] == 0 &][[1]]; Array[f, 30]
%Y Cf. A002975, A258250, A258333, A258374, A258375, A258401, A258882, A258883, A258884, A258885, A265726, A265727.
%K nonn
%O 1,1
%A _Douglas E. Iannucci_ and _Robert G. Wilson v_, Dec 14 2015
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