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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)).
0
480, 2688, 17640, 131712, 2095104, 3576000, 4248288, 16854816, 41055200, 400162032, 637787520, 788259840, 1839272960, 2423592576
OFFSET
1,1
COMMENTS
The nonunitary version of Erdős-Nicolas numbers (A194472).
If all the nonunitary divisors are permitted (i.e. k <= A048105(n)), then the nonunitary perfect numbers (A064591) are included.
EXAMPLE
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.~
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Sep 30 2019
STATUS
approved