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Search: id:A159838
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| A159838 |
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Numbers n such that n*s and n-n*s are prime, where s is the sum of the reciprocals of the prime factors of n with repetition. |
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| 10, 66, 70, 78, 114, 130, 154, 174, 222, 238, 282, 310, 318, 370, 390, 418, 474, 510, 574, 618, 642, 670, 678, 690, 742, 754, 790, 798, 814, 822, 870, 874, 930, 978, 1090, 1122, 1162, 1182, 1218, 1230, 1374, 1378, 1398, 1434, 1498, 1542, 1554, 1570, 1578
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For n to qualify it is necessary, that the sum of these reciprocals is less than one. For example, 350 = 2*5*5*7 with sum of reciprocals 1/2 + 1/5 + 1/5 + 1/7 = 73/70 which is greater than 1.
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EXAMPLE
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Take 238 = 2*7*17 with sum of reciprocals 1/2 + 1/7 + 1/17 = 167/238, giving 238*(167/238) = 167 and 238-167=71. Both 167 and 71 are prime.
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PROGRAM
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(MAGMA) T:=[ Integers()!(n*&+[ d[2]/d[1]: d in Factorization(n) ]): n in [2..1600] ]; [ k+1: k in [1..#T] | IsPrime(s) and IsPrime((k+1-s)) where s is T[k] ];
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CROSSREFS
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Cf. A001414, A000254, A024451.
Sequence in context: A000453 A097791 A140362 this_sequence A024391 A074362 A080421
Adjacent sequences: A159835 A159836 A159837 this_sequence A159839 A159840 A159841
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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), Apr 23 2009
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EXTENSIONS
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Edited, 282 and 390 inserted, extended beyond 418, MAGMA program added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 27 2009
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