login
A074919
Number of integers in {1, 2, ..., phi(n)} that are coprime to n.
4
1, 1, 2, 1, 4, 1, 6, 2, 4, 2, 10, 1, 12, 3, 5, 4, 16, 2, 18, 3, 7, 5, 22, 3, 16, 6, 12, 5, 28, 2, 30, 8, 13, 8, 17, 4, 36, 9, 15, 6, 40, 3, 42, 9, 13, 11, 46, 5, 36, 8, 21, 11, 52, 6, 29, 10, 23, 14, 58, 4, 60, 15, 20, 16, 36, 6, 66, 15, 29, 8, 70, 8, 72, 18, 21, 17, 47, 7, 78, 13, 36
OFFSET
1,3
COMMENTS
Compare the definition of a(n) to phi(n) = number of integers in {1, 2, ..., n} that are coprime to n.
FORMULA
a(n) = Sum_{d|n} mu(d)*floor(phi(n)/d). - Ridouane Oudra, Sep 16 2022
EXAMPLE
There are four numbers in {1, 2, ..., phi(8) = 4} that are coprime to 8, i.e. 1, 3. Hence a(8) = 2.
MAPLE
A074919 := proc(n)
local a, k ;
a := 0 ;
for k from 1 to numtheory[phi](n) do
if igcd(k, n) = 1 then
a := a+1 ;
end if;
end do:
a ;
end proc:
seq(A074919(n), n=1..30) ; # R. J. Mathar, Feb 21 2017
MATHEMATICA
h[n_] := Module[{l}, l = {}; For[i = 1, i <= EulerPhi[n], i++, If[GCD[i, n] == 1, l = Append[l, i]]]; l]; Table[Length[h[i]], {i, 1, 100}]
PROG
(PARI) a(n)=sum(k=1, eulerphi(n), 1==gcd(k, n)); \\ Joerg Arndt, Feb 21 2017
CROSSREFS
Cf. A000010.
Sequence in context: A074643 A060794 A300716 * A362232 A138009 A131755
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 04 2002
STATUS
approved