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%I #25 Sep 03 2023 10:45:18
%S 0,0,1,2,7,13,24,48,85,152,276,499,881
%N Number of primitive weird numbers (A002975) below 10^n.
%C It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN; A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. G. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.
%C Partial sums of A275492.
%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, Volume 147, February 2015, Pages 508-514.
%o (PARI) my(s=0); vector(10,n,s+=sum(n=10^n\20+1,10^n\2,is_A002975(n*2)))
%o (PARI) vector(10,n,#select(t->t<10^n,A002975)) \\ If A002975 is defined as set, vector, or list with enough terms.
%Y Cf. A002975, A006037, A258333, A258882, A275492, A275493, A275494.
%K nonn,more
%O 0,4
%A _M. F. Hasler_, Jul 30 2016
%E a(12) from _Robert G. Wilson v_, May 25 2018
%E a(10) corrected by _Amiram Eldar_, Sep 02 2023