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%I #10 Jun 19 2024 06:59:01
%S 480,2688,17640,131712,2095104,3576000,4248288,16854816,41055200,
%T 400162032,637787520,788259840,1839272960,2423592576
%N Numbers m that are equal to the sum of their first k consecutive nonunitary divisors, but not all of them (i.e k < A048105(m)).
%C The nonunitary version of Erdős-Nicolas numbers (A194472).
%C If all the nonunitary divisors are permitted (i.e. k <= A048105(n)), then the nonunitary perfect numbers (A064591) are included.
%e 480 is in the sequence since its nonunitary divisors are 2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240 and 2 + 4 + 6 + 8 + 10 + 12 + 16 + 20 + 24 + 30 + 40 + 48 + 60 + 80 + 120 = 480.~
%t ndivs[n_] := Block[{d = Divisors[n]}, Select[d, GCD[ #, n/# ] > 1 &]]; ndivs2[n_] := Module[{d=ndivs[n]},If[Length[d]<2,{},Drop[d, -1] ]]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n,ndivs2[n]]; a = {}; Do[ If[selDivs[n] == 0, AppendTo[a, n]; Print[n]], {n, 2, 10^6}]; a (* after _Alonso del Arte_ at A194472 *)
%Y Cf. A048105, A064591, A064597, A064599.
%Y Cf. A194472, A293618, A309843.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Sep 30 2019
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