A065219 Number of subsets of proper divisors of numbers in A065218 summing to the number.

0, 1, 2, 5, 7, 10, 34, 278, 751, 2157, 22208, 676327, 2225346, 23259536, 265050967, 39161483067, 70455119174849, 776384598617893, 133991542908557129, 21819590324155207874, 263763825614848727692, 12883245190231409112736, 661394651111310011564685

Offset: 1

Author

Jud McCranie, Oct 21 2001

Keywords

• nonn

Comments

The numbers themselves are in A065218.

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 2 is in the sequence (and 12 is in A065218).
		

Crossrefs

Cf. A065218, A064771, A063205, A005835, A002182, A004394.

Programs

Mathematica

Union@ FoldList[Max, Array[Block[{dd = Most@ Divisors@ #, c, cc}, cc = Array[c, Length@ dd]; Length@{ ToRules[Reduce[And @@ (0 <= # <= 1 &) /@ cc && dd.cc == #, cc, Integers]]}] &, 360]] (* Michael De Vlieger, Oct 01 2017, after Jean-François Alcover at A065205 *)

Formula

a(n) = A065205(A065218(n)).

Extensions

Extended by Max Alekseyev, May 29 2009

Initial 0 prepended and offset corrected by Amiram Eldar, Oct 01 2017