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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 (list; graph; refs; listen; history; text; internal format)
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 d|n}.

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 non-semiprime examples. R. J. Mathar, Jan 06 2009

STATUS

approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)