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

1,1

Comments

All terms of this sequence are even and squarefree.

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A140776, A140777, A294925.

Sequence in context: A112861 A180230 A186296 * A077064 A080715 A034168

Adjacent sequences: A140772 A140773 A140774 * A140776 A140777 A140778

Keyword

nonn

Author

Leroy Quet, May 29 2008

Extensions

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

Definition edited by Robert Israel, Jan 09 2024

Status

approved