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

1,3

Comments

The numbers themselves are in A065218.

Links

Table of n, a(n) for n=1..23.

Formula

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

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

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 *)

Crossrefs

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

Sequence in context: A226650 A024374 A297103 * A013660 A257325 A020484

Adjacent sequences: A065216 A065217 A065218 * A065220 A065221 A065222

Keyword

nonn

Author

Jud McCranie, Oct 21 2001

Extensions

Extended by Max Alekseyev, May 29 2009

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

Status

approved