A243016 Number of solutions for k*n/(k+n) = p for integer k > 0 and prime p.

0, 0, 1, 2, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1

Offset

1,4

Comments

It is unknown whether a(6) = 3 is the highest number in this sequence.

Links

Table of n, a(n) for n=1..92.

Example

4*k/(4+k) has two solutions: k=4,p=2 and k=12,p=3. Thus a(4) = 2.

Prog

(PARI) a(n) = {t=0; for(k=1, n*(n-1), s=k*n/(k+n); if(floor(s)==s, if(ispseudoprime(s), t+=1))); return(t); }
n=1; while(n<100, print1(a(n), ", "); n+=1)

Crossrefs

Sequence in context: A175663 A240672 A352288 * A284975 A219202 A341980

Adjacent sequences: A243013 A243014 A243015 * A243017 A243018 A243019

Keyword

nonn

Author

Derek Orr, May 29 2014

Status

approved