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A250034 Numerators a(n) of the rational-valued function s(n) defined below.

%I A250034 #11 Dec 02 2014 17:18:34
%S A250034 1,3,11,7,38,16,117,269,877,1003,11243,4261,56163,61883,199663,107339,
%T A250034 1839778,2009948,38444267,41354174,43432679,46078049,1064644972,
%U A250034 379669754,387106183,407127338,1258564159,1322304979,38458390826,40830611677,1268983808602
%N A250034 Numerators a(n) of the rational-valued function s(n) defined below.
%C A250034 a(n) is the numerator (after normalization) of the rational function s(n) = 1-sum(k>0,(-1)^k*sum(p1<p2<..<pk,floor(n/(p1*p2*..*pk))/(p1*p2*..*pk))), with p1,p2,..,pk being any k-tuplet of increasing prime numbers. The denominators of s(n) appear to coincide with A072155 (tested up to n=10000). For more information, see also A250031 and A250032.
%H A250034 Stanislav Sykora, <a href="/A250034/b250034.txt">Table of n, a(n) for n = 1..1000</a>
%H A250034 S. Sykora, On some number densities related to coprimes, Stan's Library, Vol.V, Nov 2014, DOI: <a href="http://dx.doi.org/10.3247/SL5Math14.005">10.3247/SL5Math14.005</a>
%e A250034 n=4: s(4) = 1 - (-1)*(floor(4/2)/2 + floor(4/3)/3)    = 1 + 1 + 1/3  = 7/3, with a(4) = 7 and 3 is indeed A072155(4). - _Wolfdieter Lang_, Dec 02 2014
%o A250034 (PARI) s_aux(n,p0,inp)={my(t=0/1,tt=0/1,in=inp,pp);while(1,pp=p0*prime(in);tt=n\pp;if(tt==0,break,t+=tt/pp-s_aux(n,pp,in++)));return(t)};
%o A250034 s(n)=1+s_aux(n,1,1);
%o A250034 a=vector(1000,n,numerator(s(n)))
%Y A250034 Cf. A250031, A250032, A250033.
%K A250034 nonn,frac
%O A250034 1,2
%A A250034 _Stanislav Sykora_, Nov 16 2014