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Search: id:A153326
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| A153326 |
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Composite numbers n such that n+1+d is prime for all nontrivial divisors d which divide n. |
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+0
1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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
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FORMULA
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{n: n+1+d in A000040 for all 1<d<n with d|n}.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A053810 A076702 A051761 this_sequence A114377 A115697 A075783
Adjacent sequences: A153323 A153324 A153325 this_sequence A153327 A153328 A153329
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KEYWORD
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easy,nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Dec 23 2008
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EXTENSIONS
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Added 4, replaced 121 by 125, extended, simplified definition, added non-semiprime examples. R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 06 2009
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