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.

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

Offset: 1

Author

Jud McCranie, Oct 21 2001

Keywords

• nonn

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.

Examples

			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.
		

Links

• Michael De Vlieger, Correlation of A065218 and A065219.

Crossrefs

Cf. A065219, A064771, A063205, A005835, A002182, A004394.

Programs

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 *)

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