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

1,2

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

Table of n, a(n) for n=1..39.

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