A307161 Numbers n such that A307159(n) = Sum_{k=1..n} bsigma(k) is divisible by n, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).

1, 2, 17, 37, 50, 56, 391, 919, 1399, 2829, 6249, 13664, 28829, 62272, 67195, 585391, 5504271, 6798541, 10763933, 866660818, 3830393407, 11044287758, 23058607363, 83159875881, 206501883259, 297734985607, 1087473543732, 1184060078117, 2789730557061, 2821551579466, 3529184155643

Offset: 1

Author

Amiram Eldar, Mar 27 2019

Keywords

• nonn

Comments

The bi-unitary version of A056550.

The corresponding quotients are 1, 2, 13, 28, 38, 43, ... (see the link for more values).

a(32) > 10^13. - Giovanni Resta, May 28 2019

Links

• Amiram Eldar and Giovanni Resta, Table of n, a(n), A307159(a(n))/a(n) for n=1..31

Crossrefs

Cf. A056550, A064611, A188999, A307043, A307159.

Programs

Mathematica

fun[p_,e_] := If[OddQ[e],(p^(e+1)-1)/(p-1),(p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); seq={};s = 0; Do[s = s + bsigma[n]; If[Divisible[s,n], AppendTo[seq,n]], {n, 1, 10^6}]; seq

Extensions

a(23)-a(31) from Giovanni Resta, Apr 20 2019