A242933 Even numbers m such that m*k/(k+m) 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 m were an odd number, k*m/(k+m) 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.

This is true (see Fried link). - Sela Fried, Mar 23 2026

Links

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

Sela Fried, Proof of a conjecture stated in A242933, 2026.

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) f(n)=for(k=1, n*(n-1), s=(k*n)/(k+n); if(floor(s)==s, if(ispseudoprime(s), return(k)))) \\ A242834
n=1; while(n<300, if(f(2*n)==0, print1(2*n, ", ")); n+=1)

Crossrefs

Cf. A242932, A242834.

Sequence in context: A067555 A108705 A127871 * A321308 A109210 A056707

Adjacent sequences: A242930 A242931 A242932 * A242934 A242935 A242936

Keyword

nonn

Author

Derek Orr, May 27 2014

Extensions

Name clarified by Michel Marcus, Mar 23 2026

Status

approved