

A220355


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


1



1, 2, 3, 5, 6, 7, 10, 15, 17, 19, 23, 34, 38, 39, 46, 47, 57, 59, 61, 78, 79, 177, 203, 209, 214, 249, 354, 371, 373, 501, 663, 755, 890, 922, 986, 1015, 1041, 1118, 1383, 1687, 1802, 1994, 2042, 2567, 2778, 3239, 3387, 3445, 3462, 3466, 4206, 4322, 4837, 5811
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OFFSET

1,2


COMMENTS

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


LINKS

Michael B. Porter, Table of n, a(n) for n = 1..60 with data from Thomas Ordowski, Marek Wolf, and Joerg Arndt; contains all terms <= 10^4.


EXAMPLE

6 is in the sequence because 6 + 6#/6 = 6 + 5#/6 = 6 + 30/6 = 11 is prime.
4 is not in the sequence because 4 + 4#/4 = 4 + 6/4 = 11/2 is not an integer.
11 is not in the sequence because 11 + 11#/11 = 11 + 7# = 11 + 210 = 221 is not prime (221 = 13 * 17).


PROG

(PARI)
pp(n) = { my(r=1); forprime(p=2, n, r*=p); r; }
/* we need to take care about n+pp(n)/n not always being integral: */
is(n) = { my(r=n+pp(n)/n); return( (type(r)==type(1)) && ispseudoprime(r) ); }
for (n=1, 10^4, if ( is(n), print1(n, ", ") ) );
/* Joerg Arndt, Apr 14 2013 */


CROSSREFS

Cf. A005117, A034386.
Sequence in context: A018336 A194359 A277006 * A059041 A129128 A164922
Adjacent sequences: A220352 A220353 A220354 * A220356 A220357 A220358


KEYWORD

nonn


AUTHOR

Thomas Ordowski, Apr 13 2013


EXTENSIONS

a(22)a(35) from Marek Wolf, Apr 14 2013
a(36)a(54) from Joerg Arndt, Apr 14 2013


STATUS

approved



