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

1,2

Comments

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.

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

Example

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

Prog

(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)))

Crossrefs

Cf. A250031, A250032, A250033.

Sequence in context: A083557 A119324 A322364 * A378678 A006495 A112286

Adjacent sequences: A250031 A250032 A250033 * A250035 A250036 A250037

Keyword

nonn,frac

Author

Stanislav Sykora, Nov 16 2014

Status

approved