A242933 Numbers n such that k*n/(k+n) is never prime for all k.

2, 16, 28, 36, 40, 50, 52, 64, 66, 70, 76, 78, 88, 92, 96, 100, 112, 116, 120, 124, 126, 130, 136, 144, 148, 154, 156, 160, 162, 170, 172, 176, 184, 186, 188, 190, 196, 204, 208, 210, 216, 220, 222, 232, 236, 238, 244, 246, 248, 250, 256, 260, 266, 268, 276, 280, 286

Offset

1,1

Comments

If n were an odd number, k*n/(k+n) would never be prime for all k; these are trivial and are not included. See A242932.

It is believed that numbers in A016742 (except 4) are members of this sequence.

Links

Table of n, a(n) for n=1..57.

Example

16*k/(16+k) is an integer for k = 16, 48, 112, and 240. These k-values give the integers 8, 12, 14, and 15, respectively. Since none are prime, 16 is a member of this sequence.

Prog

(PARI) a(n)=for(k=1, n*(n-1), s=(k*n)/(k+n); if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<300, if(a(2*n)==0, print1(2*n, ", ")); n+=1)

Crossrefs

Cf. A242932.

Sequence in context: A108705 A113933 A127871 * A321308 A109210 A056707

Adjacent sequences: A242930 A242931 A242932 * A242934 A242935 A242936

Keyword

nonn

Author

Derek Orr, May 27 2014

Status

approved