A243064 Numbers n such that k*n/(k+n) and k*n/(k-n) are integers for only one k > 0.

3, 4, 8, 9, 10, 16, 27, 32, 33, 35, 39, 44, 50, 51, 52, 55, 57, 64, 68, 69, 76, 81, 87, 88, 91, 92, 93, 104, 111, 116, 117, 123, 124, 128, 129, 130, 141, 143, 148, 152, 154, 159, 164, 170, 172, 175, 176, 177, 182, 183, 184, 188, 201, 207, 208, 212, 213, 219, 230, 232, 236, 237

Offset

1,1

Comments

a(n) = numbers n such that A243046(n) = 1.

Links

Table of n, a(n) for n=1..62.

Example

4*k/(4+k) and 4*k/(4-k) can both be integers only when k <= 4*3 = 12. Plugging in k = 1, 2, 3, ... 12, one can see that only k = 12 works for both of these expressions (3 and -6, respectively). So 4 is a member of this sequence.

Prog

(PARI) a(n)={t=0; for(k=1, n*(n-1), if(k!=n, if((k*n)%(k+n)==0&&(k*n)%(k-n)==0, t+=1))); return(t)}
n=1; while(n<300, if(a(n)==1, print1(n, ", ")); n+=1)

Crossrefs

Cf. A243046.

Sequence in context: A275096 A109826 A228145 * A057549 A284392 A047460

Adjacent sequences: A243061 A243062 A243063 * A243065 A243066 A243067

Keyword

nonn

Author

Derek Orr, May 30 2014

Status

approved