A099475 Number of divisors d of n such that d+2 is also a divisor of n.

0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 3, 0, 0, 2, 1, 0, 1, 0, 1, 1, 0, 0, 4, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 1, 3, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 4, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 5, 0, 0, 2, 1, 0, 1, 0, 1, 1, 1, 0, 4, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 0, 4, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 4, 0, 0, 2, 1, 0, 1, 0, 1, 3

Offset

1,12

Comments

Number of r X s rectangles with integer sides such that r < s, r + s = 2n, r | s and (s - r) | (s * r). - Wesley Ivan Hurt, Apr 24 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

0 <= a(n) <= a(m*n) for all m>0;

a(A099477(n)) = 0; a(A059267(n)) > 0;

a(A099476(n)) = n and a(m) <> n for m < A099476(n).

For n>0: a(A008585(n))>0, a(A008586(n))>0 and a(A008588(n))>0.

a(n) = Sum_{i=1..n-1} chi((2*n-i)/i) * chi(i*(2*n-i)/(2*n-2*i)), where chi(n) = 1 - ceiling(n) + floor(n). - Wesley Ivan Hurt, Apr 24 2020

Maple

A099475:= proc(n)
local d;
  d:= numtheory:-divisors(n);
nops(d intersect map(`+`, d, 2))
end proc:
map(A099475, [$1..1000]); # Robert Israel, Jun 19 2015

Mathematica

a[n_] := DivisorSum[n, Boole[Divisible[n, #+2]]&]; Array[a, 105] (* Jean-François Alcover, Dec 07 2015 *)

Prog

(PARI) A099475(n) = { sumdiv(n, d, ! (n % (d+2))) } \\ Michel Marcus, Jun 18 2015

Crossrefs

Cf. A007862 (similar but with d+1 instead).

Cf. A008585, A008586, A008588.

Cf. A059267, A099476, A099477.

Sequence in context: A096936 A115979 A067168 * A120569 A128113 A108930

Adjacent sequences: A099472 A099473 A099474 * A099476 A099477 A099478

Keyword

nonn,easy

Author

Reinhard Zumkeller, Oct 18 2004

Status

approved