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A298759
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Numbers k such that bphi(k) = k/2, where bphi is the bi-unitary analog of Euler's totient function (A116550).
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0
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OFFSET
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1,1
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COMMENTS
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With Euler's totient function, phi(k) = k/2 only for powers of 2 (A000079, except for 1). With the unitary totient function (A047994) the corresponding sequence is A030163.
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LINKS
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EXAMPLE
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42 is in the sequence since bphi(42) = 21 = 42/2.
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MATHEMATICA
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bphi[1] = 1; bphi[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; aQ[n_] := bphi[n] == n/2; Select[Range[10000], aQ]
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PROG
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(PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
bphi(n) = if (n==1, 1, sum(k=1, n-1, gcud(n, k) == 1));
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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