This site is supported by donations to The OEIS Foundation.



"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A250031 a(n) is the numerator of the density of natural numbers m such that gcd(m,floor(m/n))=1. 6
0, 1, 1, 13, 8, 26, 19, 163, 361, 1223, 1307, 16477, 5749, 83977, 88267, 280817, 147916, 1377406, 2839897, 58552633, 60492571, 63263911, 65468386, 403117367, 549883871, 579629587, 596790577, 1864736021, 1912541636, 29293503812, 59449633388, 969992016739 (list; graph; refs; listen; history; text; internal format)



For introduction, see the comments in A250032. The present sequence is obtained when the condition P(m) is identified, for each chosen n>0, with the equality gcd(m,floor(m/n))=1, i.e., P(m)=1 when the equality holds, while P(m)=0 when it does not. Again, the densities d(n) exist and are rational numbers. The value of a(n) is the numerator of d(n), while A250033(n) is the denominator of d(n).


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


For n>1, a(n)=A250033(n)-A250032(n), and a(n)/A250033(n)=1-s(n-1)/n, where s(n) A250034(n)/A072155(n).

lim(n->infinity)a(n)/A250033(n) = 1/zeta(2) = A059956.


When n=10, the density of numbers m that are coprime to floor(m/10) turns out to be 1223/2100. Hence a(10) = 1223/2100.

When n=2, all odd numbers qualify, but only the m=2 among even numbers does; hence the density is 1/2 and therefore a(2)=1.

When n=1, only m=1 qualifies, so that the density is 0, and a(1) = 0.


(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(1-s(n-1)/n))


Cf. A059956, A248499, A248501, A250032, A250033, A250034.

Sequence in context: A010216 A166522 A206610 * A066552 A206609 A281085

Adjacent sequences:  A250028 A250029 A250030 * A250032 A250033 A250034




Stanislav Sykora, Nov 16 2014



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.