OFFSET
1,1
COMMENTS
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.
a(8) > 2*10^9, if it exists. - Amiram Eldar, Jul 16 2022
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jan 26 2018
EXTENSIONS
a(7) from Amiram Eldar, Jul 16 2022
STATUS
approved