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A081357
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Sublime numbers, numbers for which the number of divisors and the sum of the divisors are both perfect.
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6
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OFFSET
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1,1
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COMMENTS
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The concept was introduced and the term "sublime numbers" was coined by Kevin Brown. a(1) was found by Brown (1995) and a(2) by Hickerson (1995). - Amiram Eldar, Jun 26 2021
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REFERENCES
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David J. Darling, The universal book of mathematics: from Abracadabra to Zeno's paradoxes, Hoboken, N.J.: Wiley, 2004, p. 307.
Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, pp. 4 and 395.
Roozbeh Hazrat, Mathematica®: A Problem-Centered Approach, Springer, 2016, exercise 5.5, p. 102.
Clifford A. Pickover, Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, Oxford University Press, 2001, p. 215.
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 1, p. 22.
Simon Singh, The Simpsons and Their Mathematical Secrets, A&C Black, 2013, p. 98.
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LINKS
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Jonny Griffiths, Lopsided numbers, Mathematical Spectrum, Vol. 43, No. 2 (2010/2011), pp. 53-54; entire issue.
Michael Joseph Halm, More Sequences, Mpossibilities, Issue 83, April 2003.
Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review.
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EXAMPLE
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a(1) = 12 because 12 + 6 + 4 + 3 + 2 + 1 = 28 is perfect and number of divisors, 6, is also perfect.
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CROSSREFS
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KEYWORD
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hard,nonn,bref,more
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AUTHOR
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STATUS
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approved
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