infinitary rel_primes and infinitary EulerPhi

[Meeussen Wouter (bkarnd)]

if infinitary divisors can be defined, then also infinitary_relative_primes
of n:

the easy way for "normal" divisors is:
relprime[n_]:=Select[Range[n],GCD[#,n]===1&]

the same using an explicit reference to the divisors of n :
chkrelprime[n_]:=Select[temp=Divisors[n];Range[n],
Intersection[Divisors[#],temp]==={1}&]

and now, we can use infinitary divisors:
irelprime[n_]:=Select[temp=iDivisors[n];Range[n],
Intersection[iDivisors[#],temp]==={1}&]

******************************
  in plain : 
the integers less than n that have no common iDivisors with n  
******************************

Table[irelprime[n],{n,2,24}]  (* starting from 2  *)

{1}
{1, 2}
{1, 2, 3}
{1, 2, 3, 4}
{1, 4, 5}
{1, 2, 3, 4, 5, 6}
{1, 3, 5, 7}
{1, 2, 3, 4, 5, 6, 7, 8}
{1, 3, 4, 7, 9}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
{1, 2, 5, 7, 9, 10, 11}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
{1, 3, 4, 5, 9, 11, 12, 13}
{1, 2, 4, 7, 8, 9, 11, 13, 14}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
{1, 3, 4, 5, 7, 11, 12, 13, 15, 16, 17}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}
{1, 2, 3, 6, 7, 9, 11, 13, 14, 16, 17, 18, 19}
{1, 2, 4, 5, 8, 9, 10, 11, 13, 16, 17, 18, 19, 20}
{1, 3, 4, 5, 7, 9, 12, 13, 15, 16, 17, 19, 20, 21}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22}
{1, 5, 7, 9, 11, 13, 16, 17, 19, 23}



easy to define the lengths as iEulerPhi[n] :  (* starting from 2   upto 128
*)
{1, 2, 3, 4, 3, 6, 4, 8, 5, 10, 7, 12, 8, 9, 15, 16, 11, 18, 13, 14, 14, 22,
10, 24, 16, 18, 19, 28, 13, 30, 20, 22, 21, 25, 26, 36, 24, 27, 18, 40, 17,
42, 32, 33, 29, 46, 34, 48, 32, 36, 39, 52, 24, 42, 27, 40, 37, 58, 30, 60,
40, 49, 48, 50, 30, 66, 51, 49, 35, 70, 34, 72, 48, 54, 57, 61, 36, 78, 63,
80, 54, 82, 44, 67, 57, 63, 43, 88, 46, 73, 70, 68, 62, 75, 45, 96, 64, 81,
77, 100, 49, 102, 51, 59, 69, 106, 58, 108, 56, 81, 92, 112, 54, 92, 90, 97,
78, 98, 40, 120, 80, 90, 96, 100, 66, 126, 64}


Wouter Meeussen
inability to let go a sterile train of thought
is called "perseverance"; too bad.
tel  +32 (0)51 332 124
fax +32 (0)51 332 175
mail: wouter.meeussen at vandemoortele.com




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