A356747 Numbers m that divide A306070(m) = Sum_{k=1..m} bphi(k), where bphi is the bi-unitary totient function (A116550).

1, 2, 141, 1035, 2388, 3973, 5157, 14160, 37023, 68861, 99889, 116106, 117939, 627400, 1561944, 1626983, 5901444, 10054091, 12260525, 32619981, 49775099

Offset: 1

Author

Amiram Eldar, Aug 25 2022

Keywords

• nonn
• more

Comments

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

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

Links

• Amiram Eldar, Table of n, a(n), A306070(a(n))/a(n) for n = 1..21.

Crossrefs

Cf. A116550, A306070.

Similar sequences: A048290, A306950.

Programs

Mathematica

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