A220355 - OEIS

%I #49 Apr 19 2013 07:56:11

%S 1,2,3,5,6,7,10,15,17,19,23,34,38,39,46,47,57,59,61,78,79,177,203,209,

%T 214,249,354,371,373,501,663,755,890,922,986,1015,1041,1118,1383,1687,

%U 1802,1994,2042,2567,2778,3239,3387,3445,3462,3466,4206,4322,4837,5811

%N Numbers n such that n + n# / n is prime, where n# = product of all primes <= n.

%C Squarefree A005117 numbers n such that n + A034386(n)/n is prime.

%H Michael B. Porter, <a href="/A220355/b220355.txt">Table of n, a(n) for n = 1..60</a> with data from _Thomas Ordowski_, Marek Wolf, and _Joerg Arndt_; contains all terms <= 10^4.

%e 6 is in the sequence because 6 + 6#/6 = 6 + 5#/6 = 6 + 30/6 = 11 is prime.

%e 4 is not in the sequence because 4 + 4#/4 = 4 + 6/4 = 11/2 is not an integer.

%e 11 is not in the sequence because 11 + 11#/11 = 11 + 7# = 11 + 210 = 221 is not prime (221 = 13 * 17).

%o (PARI)

%o pp(n) = { my(r=1); forprime(p=2,n,r*=p); r; }

%o /* we need to take care about n+pp(n)/n not always being integral: */

%o is(n) = { my(r=n+pp(n)/n); return( (type(r)==type(1)) && ispseudoprime(r) ); }

%o for (n=1, 10^4, if ( is(n), print1(n,", ") ) );

%o /* _Joerg Arndt_, Apr 14 2013 */

%Y Cf. A005117, A034386.

%K nonn

%O 1,2

%A _Thomas Ordowski_, Apr 13 2013

%E a(22)-a(35) from Marek Wolf, Apr 14 2013

%E a(36)-a(54) from _Joerg Arndt_, Apr 14 2013