A356747 - OEIS

A356747

Numbers m that divide A306070(m) = Sum_{k=1..m} bphi(k), where bphi is the bi-unitary totient function (A116550).

%I #8 Aug 26 2022 07:30:06

%S 1,2,141,1035,2388,3973,5157,14160,37023,68861,99889,116106,117939,

%T 627400,1561944,1626983,5901444,10054091,12260525,32619981,49775099

%N Numbers m that divide A306070(m) = Sum_{k=1..m} bphi(k), where bphi is the bi-unitary totient function (A116550).

%C The corresponding quotients A306070(m)/m are 1, 1, 57, 418, ... (see the link for more values).

%C a(22) > 6.5*10^8, if it exists.

%H Amiram Eldar, <a href="/A356747/a356747.txt">Table of n, a(n), A306070(a(n))/a(n) for n = 1..21</a>.

%t phi[x_, n_] := DivisorSum[n, MoebiusMu[#]*Floor[x/#] &]; bphi[n_] := DivisorSum[n, (-1)^PrimeNu[#]*phi[n/#, #] &, CoprimeQ[#, n/#] &]; seq = {}; s = 0; Do[s = s + bphi[n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq

%Y Cf. A116550, A306070.

%Y Similar sequences: A048290, A306950.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Aug 25 2022