

A077150


Number of composite numbers between n and 2n that are coprime to n.


2



0, 0, 1, 0, 3, 0, 4, 2, 3, 0, 7, 0, 9, 3, 4, 3, 12, 2, 14, 4, 7, 4, 17, 2, 14, 6, 11, 5, 22, 1, 23, 9, 13, 8, 16, 3, 27, 9, 15, 6, 31, 2, 33, 11, 14, 12, 37, 7, 32, 10, 21, 12, 41, 6, 27, 11, 22, 14, 45, 3, 48, 18, 24, 19, 35, 6, 53, 19, 30, 9, 56, 10, 59, 23, 26
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OFFSET

1,5


COMMENTS

It can be proved that 12 is the largest number n such that a(n) = 0.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = phi(n) + Pi(n)  Pi(2n).  Charles R Greathouse IV, May 18 2011


EXAMPLE

a(5) = 3 as there are 3 coprime (to 5) composite numbers between 5 and 10, i.e., 6, 8 and 9.


MAPLE

A077150 := proc(n) local k, s: s:=0: for k from n+1 to 2*n1 do if(not isprime(k) and gcd(k, n)=1)then s:=s+1: fi: od: return s: end: seq(A077150(n), n=1..100); # Nathaniel Johnston, May 18 2011


PROG

(PARI) for(k=1, 100, s=0:for(n=k+1, 2*k1, if(!isprime(n), if(gcd(n, k)==1, s=s+1))):print1(s", "))
(PARI) a(n)=eulerphi(n)+primepi(n)primepi(2*n) \\ Charles R Greathouse IV, May 18 2011


CROSSREFS

Sequence in context: A081170 A201291 A272192 * A065453 A152770 A098601
Adjacent sequences: A077147 A077148 A077149 * A077151 A077152 A077153


KEYWORD

nonn,easy


AUTHOR

Amarnath Murthy, Oct 30 2002


EXTENSIONS

More terms from Ralf Stephan, Mar 18 2003


STATUS

approved



