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Search: id:A082378
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| A082378 |
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Positive integers that can be written in exactly one way as the product ab of positive integers where a+b is composite. |
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+0
1
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| 3, 4, 5, 7, 11, 12, 13, 17, 18, 19, 23, 28, 29, 31, 34, 37, 41, 43, 46, 47, 52, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 106, 107, 109, 113, 118, 127, 131, 137, 138, 139, 142, 148, 149, 151, 157, 163, 166, 167, 172, 173, 178, 179, 181, 191, 193, 197, 199
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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n is in the sequence if either: 1) n is an odd prime 2) n = 2 p where p is an odd prime and exactly one of 1+2p and 2+p is prime 3) n = 4 p where p is an odd prime and both 2p+1 and 2+p are prime
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EXAMPLE
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12 is included because of 1+12, 2+6, 3+4, only 2+6 is composite;
16 is not because 2+8 and 4+4 are both composite.
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MAPLE
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S:= NULL: for n from 1 to maxN do ct:= 0; for d in numtheory[divisors](n) do if d^2 > n then next fi; if not isprime(d+n/d) then ct:= ct+1; if ct > 1 then break fi fi; od; if ct = 1 then S:= S, n fi; od: S;
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CROSSREFS
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Sequence in context: A020486 A091428 A047499 this_sequence A046642 A140826 A081735
Adjacent sequences: A082375 A082376 A082377 this_sequence A082379 A082380 A082381
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KEYWORD
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easy,nonn
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AUTHOR
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Robert Israel (israel(AT)math.ubc.ca), Sep 03 2004
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