The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A126080 a(n) = number of positive integers < n that are coprime to exactly one prime divisor of n. 4
 0, 1, 2, 2, 4, 3, 6, 4, 6, 5, 10, 6, 12, 7, 6, 8, 16, 9, 18, 10, 8, 11, 22, 12, 20, 13, 18, 14, 28, 7, 30, 16, 12, 17, 10, 18, 36, 19, 14, 20, 40, 9, 42, 22, 18, 23, 46, 24, 42, 25, 18, 26, 52, 27, 14, 28, 20, 29, 58, 14, 60, 31, 24, 32, 16, 13, 66, 34, 24, 11, 70, 36, 72, 37, 30, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 FORMULA a(p) = p - 1. EXAMPLE Concerning a(12): 1,5,7,11 are coprime to each prime dividing 12; so these integers are not counted. 6 is coprime to 0 primes dividing 12; so this integer is not counted. But the 6 integers 2,3,4,8,9,10 are each coprime to exactly one prime dividing 12; so a(12) = 6. Concerning a(30): Only the 7 integers 6,10,12,15,18,20,24 are each coprime to exactly one prime dividing 30. So a(30) = 7. MAPLE A126080 := proc(n) local divs, pdivs, a, i, pcnt, p; divs := numtheory[divisors](n); pdivs := []; for i from 1 to nops(divs) do if isprime(op(i, divs)) then pdivs := [op(pdivs), op(i, divs)]; fi; od; a := 0; for i from 1 to n-1 do pcnt := 0; for p from 1 to nops(pdivs) do if gcd(i, op(p, pdivs)) = 1 then pcnt := pcnt+1; fi; od; if pcnt = 1 then a := a+1; fi; od; RETURN(a); end: for n from 1 to 90 do printf("%d, ", A126080(n)); od; # R. J. Mathar, Mar 14 2007 MATHEMATICA Table[Count[Range[n - 1], k_ /; Total@ Boole@ Map[CoprimeQ[k, #] &, #] == 1] &[FactorInteger[n][[All, 1]]], {n, 76}] (* Michael De Vlieger, Sep 19 2017 *) PROG (PARI) a(n) = my(f=factor(n)); #select(x->(x==1), vector(n-1, j, sum(k=1, #f~, gcd(j, f[k, 1]) == 1))); \\ Michel Marcus, Oct 25 2017 CROSSREFS Cf. A128487, A128488. Sequence in context: A220096 A122376 A067240 * A302043 A060681 A202479 Adjacent sequences: A126077 A126078 A126079 * A126081 A126082 A126083 KEYWORD nonn AUTHOR Leroy Quet, Mar 02 2007 EXTENSIONS More terms from R. J. Mathar, Mar 14 2007 STATUS approved

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

Last modified August 9 21:21 EDT 2024. Contains 375044 sequences. (Running on oeis4.)