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Numbers not in the range of the sum of abundant divisors function.
2

%I #22 Apr 27 2017 12:06:54

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,28,29,31,

%T 33,34,35,37,39,41,43,45,46,47,49,51,53,55,57,59,61,63,65,67,69,71,73,

%U 75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139

%N Numbers not in the range of the sum of abundant divisors function.

%C Numbers which do not appear in A187795 or in A270660; that is, there is no integer N whose sum of abundant divisors is equal to a(n) for any n.

%C This is a finite sequence that contains every odd positive integer less than 945, twelve even integers with 46 being the largest, and has the prime number 20161 as its last term.

%C A048242 contains the first three primitive abundant numbers: 12, 18, 20.

%H Sin Hitotumatu, <a href="http://dx.doi.org/10.2977/prims/1195193227">On the Limit for the Representation by the Sum of Two Abundant Numbers</a>, Publications of the Research Institute for Mathematical Sciences of Kyoto University, 8 (1972/1973), 111-116.

%Y Cf. A005101, subsequence of A048242 and A263837, A048260, A187795, A270660 (complement).

%K nonn,fini

%O 1,2

%A _Timothy L. Tiffin_, Jul 13 2016