OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Paul K. Stockmeyer, Of camels, inheritance, and unit fractions, Math Horizons, 21 (2013), 8-11.
FORMULA
{k > 0 : 0 < [x^k] Product_{d divides (k+1)} (1+x^d)}. - Alois P. Heinz, Feb 04 2023
EXAMPLE
The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. Since 6 + 14 + 21 = 41, 41 is in the sequence.
The divisors of 43 are 1, 43. Since no selection of these divisors can possibly add up to 42, this means that 42 is not in the sequence.
MAPLE
q:= proc(m) option remember; local b, l; b, l:=
proc(n, i) option remember; n=0 or i>=1 and
(l[i]<=n and b(n-l[i], i-1) or b(n, i-1))
end, sort([numtheory[divisors](m+1)[]]);
b(m, nops(l)-1)
end:
select(q, [$1..300])[]; # Alois P. Heinz, Feb 04 2023
MATHEMATICA
divNextableQ[n_] := TrueQ[Length[Select[Subsets[Divisors[n + 1]], Plus@@# == n &]] > 0]; Select[Range[100], divNextableQ] (* Alonso del Arte, Jan 07 2023 *)
PROG
(Scala) def divisors(n: Int): IndexedSeq[Int] = (1 to n).filter(n % _ == 0)
def divPartSums(n: Int): List[Int] = divisors(n).toSet.subsets.toList.map(_.sum)
(1 to 128).filter(n => divPartSums(n + 1).contains(n)) // Alonso del Arte, Jan 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 03 2003
STATUS
approved