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 A283550 Numbers that are not the sum of abundant numbers (not necessarily distinct). 4

%I #23 Mar 27 2017 19:41:17

%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

%N Numbers that are not the sum of abundant numbers (not necessarily distinct).

%C a(496) = 991 is the last term.

%C Subsequence of A048242 (Numbers that are not the sum of two abundant numbers).

%C Giovanni Resta noticed that 991 is the largest number that is not a sum of abundant numbers.

%H Amiram Eldar, <a href="/A283550/b283550.txt">Table of n, a(n) for n = 1..496</a>

%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/abundant_number/">abundant numbers</a>

%e 20161 = 12 + 304 + 19845 is the sum of 3 abundant numbers and thus not in the sequence (although it is in A048242, since it is not the sum of 2 abundant numbers).

%t AbundantQ[n_] := DivisorSigma[1, n] > 2 n; a = Select[Range[1000], AbundantQ[#] &]; nn = Dimensions[a][[1]]; t = Rest[CoefficientList[ Series[Product[(1 + x^a[[k]]), {k, nn}], {x, 0, a[[-1]]}], x]]; f = Flatten[Position[t, 0]]

%Y Cf. A271113, A048242, A005101.

%K nonn,fini,full

%O 1,2

%A _Amiram Eldar_, Mar 10 2017

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)