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 A065218 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. 10
 1, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 831600, 1081080, 1441440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Indices of records in A065205 and A033630. The corresponding records (number of subsets) are in A065219. This sequence is not a subset of A002182: 831600 belongs to this sequence but not A002182. LINKS Michael De Vlieger, Correlation of A065218 and A065219. EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A065219, A064771, A063205, A005835, A002182, A004394. Sequence in context: A249127 A277336 A140522 * A187678 A124509 A319127 Adjacent sequences:  A065215 A065216 A065217 * A065219 A065220 A065221 KEYWORD nonn AUTHOR Jud McCranie, Oct 21 2001 EXTENSIONS More terms from Franklin T. Adams-Watters, Nov 27 2006 Edited and extended by Max Alekseyev, May 29 2009 Offset changed by Andrey Zabolotskiy, Oct 10 2017 STATUS approved

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Last modified September 28 11:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)