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%I #19 Feb 26 2024 07:39:24
%S 1,2,29,181,442,425,850,1300,2600,3250,5525,11050,17425,16900,44100,
%T 18850,72250,44200,122525,75400,55250,110500,237250,188500,266500,
%U 397800,375700,377000,187850,221000,469625,718250,640900,1105000,1812200,2340900,751400,3591250
%N The smallest number k that can be partitioned in n ways as the sum of two numbers from A020487.
%H Michael S. Branicky, <a href="/A369384/b369384.txt">Table of n, a(n) for n = 0..106</a>
%e a(0) = 1 because 1 cannot be written as the sum of two terms in A020487.
%e 2 = 1 + 1 = A020487(1) + A020487(1), so a(1) = 2.
%e The numbers 3, 4, ..., 28 can be written as the sum of two terms in A020487 in at most one way and 29 = 4 + 25 = A020487(2) + A020487(6) and 29 = 9 + 20 = A020487(3) + A020487(5), so a(2) = 29.
%o (Magma) ant:=func<n|IsZero(DivisorSigma(2, n) mod DivisorSigma(1, n))>; b:=[n: n in [1..700000] |ant(n)]; a:=[]; for n in [0..30] do k:=1; while #RestrictedPartitions(k,2,Set(b)) ne n do k:=k+1; end while; Append(~a,k); end for; a;
%Y Cf. A000203, A001157, A020487.
%K nonn
%O 0,2
%A _Marius A. Burtea_, Jan 25 2024
%E a(16) corrected and more terms from _Michael S. Branicky_, Feb 24 2024
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