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Search: id:A138302
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| 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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These numbers are called "compact integers". They consist of 1 and the positive integers for which all exponents of primes in its prime power factorization are nonnegative powers of 2.
The density of this sequence exists and equals 0.872497...
There exist only seven compact factorials A000142(n) for n=1,2,3,6,7,10 and 11.
#1. All natural numbers except cubes, 2^3=8, 3^3=27, 4^3=64, ... are missing from the current sequence. #2. Sorted A104492 Cube excess of the n-th prime = A138302. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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REFERENCES
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V. Shevelev, Compact integers and factorials. Acta Arithmetica,126,no.3(2007), 195-236.
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LINKS
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S. Litsyn and V. Shevelev, On Factorization of Integers with Restrictions on the Exponents, INTEGERS: The Electronic Journal ofCombinatorial Number Theory 7(2007),#A33.
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MATHEMATICA
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lst={}; Do[p=Prime[n]; s=p^(1/3); f=Floor[s]; a=f^3; d=p-a; AppendTo[lst, d], {n, 7!}]; Union[lst] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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CROSSREFS
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Cf. A084400, A050376, A005117.
Cf. A104492 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
Sequence in context: A102352 A007412 A096432 this_sequence A171524 A052421 A037477
Adjacent sequences: A138299 A138300 A138301 this_sequence A138303 A138304 A138305
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 07 2008
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