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%I #18 May 28 2019 03:47:18
%S 1,2,17,37,50,56,391,919,1399,2829,6249,13664,28829,62272,67195,
%T 585391,5504271,6798541,10763933,866660818,3830393407,11044287758,
%U 23058607363,83159875881,206501883259,297734985607,1087473543732,1184060078117,2789730557061,2821551579466,3529184155643
%N 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).
%C The bi-unitary version of A056550.
%C The corresponding quotients are 1, 2, 13, 28, 38, 43, ... (see the link for more values).
%C a(32) > 10^13. - _Giovanni Resta_, May 28 2019
%H Amiram Eldar and Giovanni Resta, <a href="/A307161/a307161_2.txt">Table of n, a(n), A307159(a(n))/a(n) for n=1..31</a>
%t 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
%Y Cf. A056550, A064611, A188999, A307043, A307159.
%K nonn
%O 1,2
%A _Amiram Eldar_, Mar 27 2019
%E a(23)-a(31) from _Giovanni Resta_, Apr 20 2019
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