

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
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OFFSET

1,3


LINKS



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 n1 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(n1, j, sum(k=1, #f~, gcd(j, f[k, 1]) == 1))); \\ Michel Marcus, Oct 25 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



