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Search: id:A007964
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| A007964 |
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Numbers n such that product of proper divisors of n is <= n; i.e. product of divisors of n is <= n^2. |
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+0
4
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Smarandache and others call these "simple numbers".
Numbers which are the product of up to two primes (not necessarily distinct) or the cube of a prime. Alternatively, numbers having prime decomposition p*q, where q either is distinct from p or equals p^k for 0<=k<=2.
Corresponds to numbers having at most four divisors. (For numbers with exactly four divisors see A030513) - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 23 2003
For n>3: numbers that can occur as fourth divisors; union of A000040, A001248, A006881, and A030078. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 15 2006
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REFERENCES
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Liu Hongyan and Zhang Wenpeng, On the simple numbers and the mean value properties, Smarandache Notions (Book Series, Vol. 14), American Research Press, 2004; pp. 171-175.
F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
F. Smarandache, Only Problems, Not Solutions!.
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CROSSREFS
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Cf. A007955, A058080.
Sequence in context: A064683 A084384 A119885 this_sequence A095135 A135402 A135393
Adjacent sequences: A007961 A007962 A007963 this_sequence A007965 A007966 A007967
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KEYWORD
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nonn,easy
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AUTHOR
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R. Muller
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EXTENSIONS
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Description corrected by Henry Bottomley (se16(AT)btinternet.com), Nov 24 2000
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