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 A116550 The bi-unitary analog of Euler's totient function of n. 9
 1, 1, 2, 3, 4, 3, 6, 7, 8, 6, 10, 8, 12, 9, 9, 15, 16, 12, 18, 14, 14, 15, 22, 17, 24, 18, 26, 21, 28, 15, 30, 31, 23, 24, 25, 29, 36, 27, 28, 31, 40, 21, 42, 35, 34, 33, 46, 36, 48, 36, 37, 42, 52, 39, 42, 46, 42, 42, 58, 34, 60, 45, 51, 63, 50, 35, 66, 56, 51, 38, 70, 62, 72, 54 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(1)=1; for n>1, a(n) is the number of numbers m1, if n = product{p=primes,p|n} p^b(n,p), where each b(n,p) is a positive integer, then a(n) is number of positive integers m, m < n, such that each b(m,p) does not equal b(n,p). EXAMPLE 12 = 2^2 * 3^1. Of the positive integers < 12, there are 8 integers where no prime divides these integers the same number of times the prime divides 12: 1, 2 = 2^1, 5 = 5^1, 7 = 7^1, 8 = 2^3, 9 = 3^2, 10 = 2^1 *5^1 and 11 = 11^1. So a(12) = 8. The other positive integers < 12 (3 = 3^1, 4 = 2^2 and 6 = 2^1 * 3^1) each are divisible by at least one prime the same number of times this prime divides 12. MAPLE # returns the greatest common unitary divisor of m and n, A225174(m, n) f:=proc(m, n)    local i, ans;    ans:=1;    for i from 1 to min(m, n) do      if ((m mod i) = 0) and (igcd(i, m/i) = 1)  then        if ((n mod i) = 0) and (igcd(i, n/i) = 1)  then ans:=i; fi;      fi;    od; ans; end; A116550:=proc(n)   global f; local ct, m;   ct:=0;   if n = 1 then RETURN(1) else   for m from 1 to n-1 do     if f(m, n)=1 then ct:=ct+1; fi;   od:   fi;   ct; end; # N. J. A. Sloane, May 01 2013 A116550 := proc(n)     local a, k;     a := 0 ;     for k from 1 to n do         if A165430(k, n) = 1 then             a := a+1 ;         end if ;     end do:     a ; end proc: # R. J. Mathar, Jul 21 2016 MATHEMATICA a = 1; a[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; Table[a[n], {n, 1, 90}] (* Jean-François Alcover, Sep 05 2013 *) PROG (PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); } gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m))); a(n) = if (n==1, 1, sum(k=1, n-1, gcud(n, k) == 1)); \\ Michel Marcus, Nov 09 2017 CROSSREFS Cf. A225174, A005424, A225175, A225176, A000010, A047994. Sequence in context: A048276 A127463 A076618 * A283165 A116991 A330061 Adjacent sequences:  A116547 A116548 A116549 * A116551 A116552 A116553 KEYWORD nonn AUTHOR Leroy Quet, Mar 16 2006 EXTENSIONS More terms from R. J. Mathar, Jan 23 2008 Entry revised by N. J. A. Sloane, May 01 2013 STATUS approved

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)