A309843
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).
Original entry on oeis.org
24, 360, 4320, 14688, 1468800, 9547200, 50585472, 54198720, 189695520, 1680459264
Offset: 1
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.
-
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 *)
A327944
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)).
Original entry on oeis.org
480, 2688, 17640, 131712, 2095104, 3576000, 4248288, 16854816, 41055200, 400162032, 637787520, 788259840, 1839272960, 2423592576
Offset: 1
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.~
-
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 *)
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