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A250034 Numerators a(n) of the rational-valued function s(n) defined below. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A153285 A083557 A119324 * A006495 A112286 A126261

Adjacent sequences:  A250031 A250032 A250033 * A250035 A250036 A250037

KEYWORD

nonn,frac

AUTHOR

Stanislav Sykora, Nov 16 2014

STATUS

approved

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Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.