A085496 Number of ways to write prime(n) as sum of distinct divisors of prime(n)+1.

0, 1, 1, 1, 2, 0, 1, 1, 5, 3, 1, 0, 2, 0, 10, 1, 31, 0, 0, 26, 0, 6, 23, 20, 0, 0, 1, 13, 0, 0, 1, 15, 0, 14, 9, 0, 0, 0, 190, 0, 713, 0, 42, 0, 7, 9, 0, 9, 6, 0, 6, 2148, 0, 509, 0, 120, 109, 1, 0, 0, 0, 4, 6, 100, 0, 0, 0, 0, 2, 4, 0, 21897, 1, 0, 3, 85, 79, 0, 0, 0, 19172, 0, 1130

Offset

1,5

Comments

a(n) = A085491(A000040(n));

a(A085498(n)) > 0.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Example

n=5, divisors of A000040(5)+1=11+1=12 that are not greater 11: {1,2,3,4,6}, 11=6+4+1=6+3+2, therefore a(5)=2.

Maple

b:= proc(n, i) option remember; global l;
      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+
      `if`(l[i]>n, 0, b(n-l[i], i-1))))
    end:
a:= proc(n) global l; local p;
      forget(b);
      p:= ithprime(n);
      l:= sort([numtheory[divisors](p+1)[]]);
      b(p, nops(l)-1)
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 01 2012

Mathematica

Count[Total/@Subsets[Most[Divisors[Prime[#]+1]]], Prime[#]]&/@Range[90] (* Harvey P. Dale, Jan 31 2016 *)

Crossrefs

Sequence in context: A244677 A243986 A322838 * A228748 A343464 A225094

Adjacent sequences: A085493 A085494 A085495 * A085497 A085498 A085499

Keyword

nonn

Author

Reinhard Zumkeller, Jul 03 2003

Status

approved