A192281 Prime numbers whose anti-divisors are all prime numbers

5, 7, 11, 17, 19, 29, 43, 47, 61, 71, 79, 89, 101, 107, 109, 151, 191, 197, 223, 251, 271, 317, 349, 359, 421, 439, 461, 521, 569, 601, 631, 659, 673, 691, 701, 719, 811, 821, 881, 911, 919, 947, 971, 991, 1009, 1051, 1091, 1109, 1153, 1181, 1217, 1231

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

Anti-divisors of 109 are 2, 3, 7, 31, 73 that are all prime numbers

Maple

with(numtheory);
P:=proc(i)
local a, b, c, k, j, n, ok;
for n from 3 by 1 to i do
  j:=ithprime(n); a:={};
   for k from 2 to j-1 do
     if abs((j mod k)- k/2) < 1 then a:=a union {k}; fi;
   od;
   b:=nops(a); c:=op(a);
   if b>1 then
     ok:=1;
     for k from 1 to b do
       if (not isprime(c[k])) then ok:=0; break; fi;
     od;
     if ok=1 then print(j); fi;
   else
     if isprime(op(a)) then print(j); fi;
   fi;
od;
end:

Crossrefs

Cf. A066272

Sequence in context: A136052 A301913 A110587 * A191065 A271658 A282739

Adjacent sequences: A192278 A192279 A192280 * A192282 A192283 A192284

Keyword

nonn,easy

Author

Paolo P. Lava, Jul 15 2011

Status

approved