|
%I #6 Oct 13 2017 05:07:53
%S 24,360,432,1344,2016,19440,45360,68544,714240,864000,1468800,1571328,
%T 1900800,2391120,2888704,3057600,4586400,5241600,103194000
%N Numbers n that equal the sum of their first k consecutive aliquot bi-unitary divisors, but not all of them (i.e k < A286324(n)-1).
%C The bi-unitary version of Erdős-Nicolas numbers (A194472).
%C If all the aliquot bi-unitary divisors are permitted (i.e. k <= A286324(n)-1), then the 3 bi-unitary perfect numbers, 6, 60 and 90, are included.
%e 24 is in the sequence since its aliquot bi-unitary divisors are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24.
%t f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[bdiv[n], -2]]; a = {}; Do[ If[selDivs[n] == 0, AppendTo[a, n]; Print[n]], {n, 2, 10^6}]; a (* after Alonso del Arte at A194472 *)
%Y Cf. A188999, A194472, A222266, A286324.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Oct 13 2017
|
