A085491 Number of ways to write n as sum of distinct divisors of n+1.

1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 5, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 31, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 26, 0, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 23, 0, 0, 0, 1, 0, 20, 0, 0, 0, 0, 0, 21, 0, 0, 0, 1

Offset: 0

Author

Reinhard Zumkeller, Jul 03 2003

Keywords

• nonn

Comments

a(A085492(n)) = 0; a(A085493(n)) > 0; a(A085494(n)) = 1.

Examples

			n=11, divisors of 12=11+1 that are not greater 11: {1,2,3,4,6}, 11=6+5=6+4+1, therefore a(11)=2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A085496.

Programs

Maple

a:= proc(m) option remember; local b, l; b, l:=
      proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
        b(n, i-1)+`if`(l[i]>n, 0, b(n-l[i], i-1))))
      end, sort([numtheory[divisors](m+1)[]]);
      forget(b); b(m, nops(l)-1)
    end:
seq(a(n), n=0..120);  # Alois P. Heinz, Mar 12 2019

Mathematica

a[n_] := Module[{dd}, dd = Select[Divisors[n+1], # <= n&]; Select[ IntegerPartitions[n, dd // Length, dd], Reverse[#] == Union[#]&] // Length]; Array[a, 100, 0] (* Jean-François Alcover, Mar 12 2019 *)

Formula

a(n) = [x^n] Product_{d divides (n+1)} (1 + x^d). - Alois P. Heinz, Feb 04 2023

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 12 2019