

A075861


Least k such that (nk) divides (n+k).


6



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
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OFFSET

2,3


COMMENTS

a(n) is also the least k>0 such that F(nk) 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 kn), then a(n) is the least k>0 such that f(nk) divides f(n+k). More examples of such f(n): 2^n1, 3^n1, n^2, n^3.  Clark Kimberling, Jul 30 2012


LINKS



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, ni], i++]; i, {n, 2, 100}] (* Harvey P. Dale, Mar 28 2011 *)


PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



