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

1,2

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

Table of n, a(n) for n=1..21.

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

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

Crossrefs

Cf. A116550, A306070.

Similar sequences: A048290, A306950.

Sequence in context: A221601 A334013 A115890 * A215187 A101827 A283097

Adjacent sequences: A356744 A356745 A356746 * A356748 A356749 A356750

Keyword

nonn,more

Author

Amiram Eldar, Aug 25 2022

Status

approved