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 A099475 Number of divisors d of n such that d+2 is also a divisor of n. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 15 20:40 EDT 2021. Contains 342977 sequences. (Running on oeis4.)