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

Author

Paolo P. Lava, Jul 15 2011

Keywords

• nonn
• easy

Examples

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

Crossrefs

Cf. A066272

Programs

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: