|
|
A053343
|
|
Semiprimes of the form pq where p < q and p + q - 1 is prime.
|
|
1
|
|
|
15, 33, 35, 51, 65, 77, 87, 91, 95, 119, 123, 143, 161, 177, 185, 209, 213, 215, 217, 221, 247, 259, 287, 303, 321, 329, 335, 341, 371, 377, 395, 403, 407, 411, 427, 437, 447, 469, 473, 485, 511, 515, 527, 533, 537, 545, 551, 573, 581, 591, 611, 629, 635
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Squarefree terms of A050530 with 2 prime divisors.
|
|
LINKS
|
|
|
FORMULA
|
n=pq such that n-phi(n) = pq-(p-1)(q-1) = p+q-1 is prime.
|
|
MATHEMATICA
|
With[{nn=70}, Take[Times@@@Select[Subsets[Prime[Range[nn]], {2}], PrimeQ[Total[#] - 1] &]//Union, nn]] (* Vincenzo Librandi, Aug 23 2017 *)
|
|
PROG
|
(PARI) list(lim)=my(v=List()); forprime(p=5, lim\3, forprime(q=3, min(lim\p, p-2), if(isprime(p+q-1), listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Aug 23 2017
(GAP)
A053343:=List(Filtered(Filtered(List(Filtered(List([1..10^5], Factors), i->Length(i)=2), Set), j->Length(j)=2), i->IsPrime(Sum(i)-1)), Product); # Muniru A Asiru, Aug 29 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|