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A298759 Numbers n such that bphi(n) = n/2, where bphi is the bi-unitary analog of Euler's totient function (A116550). 0
2, 6, 30, 42, 1722, 1806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With Euler's totient function, phi(n) = n/2 only for powers of 2 (A000079, except for 1). With the unitary totient function (A047994) the corresponding sequence is A030163.

No more terms below 10^5.

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

42 is in the sequence since bphi(42) = 21 = 42/2.

MATHEMATICA

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]

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)));

bphi(n) = if (n==1, 1, sum(k=1, n-1, gcud(n, k) == 1));

isok(n) = bphi(n) == n/2; \\ Michel Marcus, Jan 26 2018

CROSSREFS

Cf. A047994, A030163, A116550.

Sequence in context: A100194 A229882 A325986 * A127517 A137825 A008341

Adjacent sequences:  A298756 A298757 A298758 * A298760 A298761 A298762

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Jan 26 2018

STATUS

approved

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Last modified June 12 14:32 EDT 2021. Contains 344957 sequences. (Running on oeis4.)