cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A298759 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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%I A298759 #11 Jul 16 2022 07:14:03
%S A298759 2,6,30,42,1722,1806,19977474
%N A298759 Numbers k such that bphi(k) = k/2, where bphi is the bi-unitary analog of Euler's totient function (A116550).
%C A298759 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.
%C A298759 a(8) > 2*10^9, if it exists. - _Amiram Eldar_, Jul 16 2022
%e A298759 42 is in the sequence since bphi(42) = 21 = 42/2.
%t A298759 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]
%o A298759 (PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
%o A298759 gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
%o A298759 bphi(n) = if (n==1, 1, sum(k=1, n-1, gcud(n, k) == 1));
%o A298759 isok(n) = bphi(n) == n/2; \\ _Michel Marcus_, Jan 26 2018
%Y A298759 Cf. A047994, A030163, A116550.
%K A298759 nonn,more
%O A298759 1,1
%A A298759 _Amiram Eldar_, Jan 26 2018
%E A298759 a(7) from _Amiram Eldar_, Jul 16 2022