

A235268


Least integer k > n such that n*k/(n+k) is an integer, or 0 if no such k exists.


2



1, 0, 0, 6, 12, 20, 12, 42, 24, 18, 15, 110, 24, 156, 35, 30, 48, 272, 36, 342, 30, 28, 99, 506, 40, 100, 143, 54, 70, 812, 45, 930, 96, 66, 255, 140, 45, 1332, 323, 78, 60, 1640, 56, 1806, 77, 90, 483, 2162, 80, 294, 75, 102, 117, 2756, 108, 66, 140, 114, 783
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


REFERENCES

a(3) = 6 because 6 is the smallest k > 3 such that k*3/(k+3) is an integer.


LINKS

Giovanni Resta, Table of n, a(n) for n = 0..1000


FORMULA

For prime p, a(p) = p*(p1) = A002378(p1).  Ralf Stephan, Jan 15 2014


MATHEMATICA

a[0]=1; a[n_] := Block[{k, s, x}, s = Reduce[k*n/(k+n) == x && k>n, {k, x}, Integers]; If[s === False, 0, Min[k /. List@ ToRules@s]]]; a/@Range[0, 100] (* Giovanni Resta, Jan 20 2014 *)


PROG

(PARI) a(n)=my(k=n+1); while((n*k)%(n+k)!=0, k=k+1); k \\ Ralf Stephan, Jan 15 2014


CROSSREFS

Cf. A063427.
Sequence in context: A233586 A332543 A348914 * A354931 A105455 A345919
Adjacent sequences: A235265 A235266 A235267 * A235269 A235270 A235271


KEYWORD

nonn


AUTHOR

Alex Ratushnyak, Jan 05 2014


STATUS

approved



