A140775 Numbers k > 1 such that p + k/p is prime for every prime p that divides k.

2, 6, 10, 22, 30, 34, 42, 58, 70, 78, 82, 102, 118, 130, 142, 190, 202, 210, 214, 274, 298, 310, 322, 330, 358, 382, 394, 442, 454, 462, 478, 510, 538, 562, 582, 610, 622, 658, 694, 714, 730, 742, 790, 838, 862, 922, 930, 970, 1002, 1038, 1042, 1110, 1138, 1198

Offset: 1

Author

Leroy Quet, May 29 2008

Keywords

• nonn

Comments

All terms of this sequence are even and squarefree.

The only term == 2 (mod 3) is 2. - Robert Israel, Jan 09 2024

Examples

			The primes dividing 70 are 2, 5, 7. Now, 2 + 70/2 = 37; 5 + 70/5 = 19; 7 + 70/7 = 17. Since 37, 19 and 17 are each prime, then 70 is included in this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A140776, A140777, A294925.

Programs

Maple

filter:= t -> andmap(p -> isprime(p+t/p), numtheory:-factorset(t)):
select(filter, [seq(i,i=2..2000,4)]); # Robert Israel, Jan 09 2024

Mathematica

fQ[n_] := Block[{p = First@ Transpose@ FactorInteger@ n}, Union@ PrimeQ[p + n/p] == {True}]; Select[ Range[2, 1221], fQ@# &] (* Robert G. Wilson v, May 30 2008 *)
pnpQ[n_]:=AllTrue[#+n/#&/@Transpose[FactorInteger[n]][[1]],PrimeQ]; Select[ Range[2,1200],pnpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 15 2016 *)

Extensions

More terms from Robert G. Wilson v, May 30 2008

Definition edited by Robert Israel, Jan 09 2024