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Search: id:A014567
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| A014567 |
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Numbers n such that n and sigma(n) are relatively prime, where sigma(n) = sum of divisors of n, A000203. |
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8
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| 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 47, 49, 50, 53, 55, 57, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 89, 93, 97, 98, 100, 101, 103, 107, 109, 111, 113, 115, 119, 121, 125, 127, 128, 129, 131, 133
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Related to "solitary numbers": n is solitary if there is no other integer m such that sigma(m)/m = sigma(n)/n.
It is easy to show that if n and sigma(n) are relatively prime then n is solitary. But the converse is not true; for example, 18, 45, 48, and 52 are solitary. Probably also 10, 14, 15, 20, 22, and many others are solitary, but I do not think that will ever be proved. - Dean Hickerson (dean(AT)math.ucdavis.edu)
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REFERENCES
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Anderson, C. W. and Hickerson, D.; Problem 6020. ``Friendly Integers.'' Amer. Math. Monthly 84, 65-66, 1977.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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sigma(21) = 1+3+7+21 = 32 is relatively prime to 21.
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MATHEMATICA
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lst={}; Do[d=DivisorSigma[1, n]; If[GCD[d, n]==1, AppendTo[lst, n]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 01 2008]
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CROSSREFS
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Cf. A003624
Adjacent sequences: A014564 A014565 A014566 this_sequence A014568 A014569 A014570
Sequence in context: A082377 A133811 A119314 this_sequence A030230 A089352 A086486
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from Labos Elemer (LABOS(AT)ana.sote.hu).
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