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

1, 3, 11, 7, 38, 16, 117, 269, 877, 1003, 11243, 4261, 56163, 61883, 199663, 107339, 1839778, 2009948, 38444267, 41354174, 43432679, 46078049, 1064644972, 379669754, 387106183, 407127338, 1258564159, 1322304979, 38458390826, 40830611677, 1268983808602

Offset: 1

Author

Stanislav Sykora, Nov 16 2014

Keywords

• nonn
• frac

Comments

a(n) is the numerator (after normalization) of the rational function s(n) = 1-sum(k>0,(-1)^k*sum(p1A072155 (tested up to n=10000). For more information, see also A250031 and A250032.

Examples

			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
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..1000
• S. Sykora, On some number densities related to coprimes, Stan's Library, Vol.V, Nov 2014, DOI: 10.3247/SL5Math14.005

Crossrefs

Cf. A250031, A250032, A250033.

Programs

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)};
s(n)=1+s_aux(n,1,1);
a=vector(1000,n,numerator(s(n)))