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%I #38 Sep 14 2019 06:36:47
%S 24,360,4320,14688,1468800,9547200,50585472,54198720,189695520,
%T 1680459264
%N Numbers m that equal the sum of their first k consecutive aliquot infinitary divisors, but not all of them (i.e k < A037445(m) - 1).
%C The infinitary version of Erdős-Nicolas numbers (A194472).
%C If all the aliquot infinitary divisors are permitted (i.e. k <= A037445(n) - 1), then the infinitary perfect numbers (A007357) are included.
%e 24 is in the sequence since its aliquot infinitary divisors are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24.
%t idivs[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[ x ] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[idivs[n], -2]]; s= {}; Do[If[selDivs[n] == 0, AppendTo[s, n]], {n, 2, 10^6}]; s(* after _Alonso del Arte_ at A194472 *)
%Y Cf. A007357, A077609, A037445, A049417, A194472, A293618.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Sep 14 2019
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