A075861 Least k such that (n-k) divides (n+k).

1, 1, 2, 3, 2, 5, 4, 3, 5, 9, 4, 11, 7, 5, 8, 15, 6, 17, 10, 7, 11, 21, 8, 15, 13, 9, 14, 27, 10, 29, 16, 11, 17, 21, 12, 35, 19, 13, 20, 39, 14, 41, 22, 15, 23, 45, 16, 35, 25, 17, 26, 51, 18, 33, 28, 19, 29, 57, 20, 59, 31, 21, 32, 39, 22, 65, 34, 23, 35, 69, 24, 71, 37, 25, 38

Offset

2,3

Comments

a(n) is also the least k>0 such that F(n-k) divides F(n+k), where F = A000045 (Fibonacci numbers). More generally, if (f(n)) is a divisibility sequence (that is, f(k)|f(n) if and only k|n), then a(n) is the least k>0 such that f(n-k) divides f(n+k). More examples of such f(n): 2^n-1, 3^n-1, n^2, n^3. - Clark Kimberling, Jul 30 2012

Links

Amiram Eldar, Table of n, a(n) for n = 2..10000

Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k)/n^2 for n = 1..10000

Formula

Sum_{i=1..n} a(i) is asymptotic to c*n^2, where c = 0.28....

Mathematica

Table[i=1; While[!Divisible[n+i, n-i], i++]; i, {n, 2, 100}]  (* Harvey P. Dale, Mar 28 2011 *)

Prog

(PARI) a(n)=if(n<0, 0, s=1; while((n+s)%(n-s)>0, s++); s)

Crossrefs

Sequence in context: A317585 A132226 A197702 * A205706 A141658 A350169

Adjacent sequences: A075858 A075859 A075860 * A075862 A075863 A075864

Keyword

nonn

Author

Benoit Cloitre, Oct 15 2002

Status

approved