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%I #17 Oct 11 2017 05:18:57
%S 1,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560,
%T 10080,15120,20160,25200,27720,45360,50400,55440,83160,110880,166320,
%U 221760,277200,332640,498960,554400,665280,720720,831600,1081080,1441440
%N Consider the subsets of proper divisors of a number that sum to the number. These are numbers that set a record number of such subsets.
%C Indices of records in A065205 and A033630. The corresponding records (number of subsets) are in A065219.
%C This sequence is not a subset of A002182: 831600 belongs to this sequence but not A002182.
%H Michael De Vlieger, <a href="/A065218/a065218.txt">Correlation of A065218 and A065219</a>.
%e Proper divisors of 12 are {1, 2, 3, 4, 6}. Two subsets of this sum to 12: {2, 4, 6} and {1, 2, 3, 6} - more than any smaller number, so 12 is in the sequence.
%t With[{s = Table[-1 + SeriesCoefficient[Series[Times @@ ((1 + z^#) & /@ Divisors[n]), {z, 0, n}], n], {n, 2520}]}, FirstPosition[s, #][[1]] & /@ Union@ FoldList[Max, s]] (* _Michael De Vlieger_, Oct 10 2017 *)
%Y Cf. A065219, A064771, A063205, A005835, A002182, A004394.
%K nonn
%O 1,2
%A _Jud McCranie_, Oct 21 2001
%E More terms from _Franklin T. Adams-Watters_, Nov 27 2006
%E Edited and extended by _Max Alekseyev_, May 29 2009
%E Offset changed by _Andrey Zabolotskiy_, Oct 10 2017
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