

A153326


Composite numbers n such that n+1+d is prime for all nontrivial divisors d which divide n.


0



4, 8, 9, 25, 27, 35, 39, 55, 65, 119, 125, 185, 203, 219, 235, 237, 289, 305, 319, 341, 415, 417, 437, 515, 535, 597, 649, 655, 671, 685, 749, 755, 905, 935, 959, 979, 989, 1003, 1043, 1079, 1111, 1119, 1165, 1227, 1247, 1285, 1299, 1315, 1343, 1355, 1465, 1469, 1565, 1649, 1681, 1735, 1739, 1829
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OFFSET

1,1


COMMENTS

4 and 8 are the only even numbers.
Numbers in the sequence which are not semiprimes: 8, 27, 125, 935, 1859, 2849 etc.  R. J. Mathar, Jan 06 2009


LINKS

Table of n, a(n) for n=1..58.


FORMULA

{n: n+1+d in A000040 for all 1<d<n with dn}.


EXAMPLE

For n=8, the nontrivial divisors are 2 and 4 and (8+1)+2 = 11 and (8+1)+4 = 13 are both prime.
For 35 the nontrivial divisors are 5 and 7. With (35+1) + 5=41 and (35+1) + 7 = 43, both sums are primes.


CROSSREFS

Sequence in context: A053810 A076702 A051761 * A168363 A182046 A171468
Adjacent sequences: A153323 A153324 A153325 * A153327 A153328 A153329


KEYWORD

easy,nonn


AUTHOR

J. M. Bergot, Dec 23 2008


EXTENSIONS

Added 4, replaced 121 by 125, extended, simplified definition, added nonsemiprime examples. R. J. Mathar, Jan 06 2009


STATUS

approved



