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Search: id:A067712
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| A067712 |
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Numbers n such that sum of exponents in prime factorization of n is > ln(n). |
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+0
1
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| 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 96, 108, 112, 120, 128, 144, 160, 192, 216, 224, 240, 256, 288, 320, 324, 336, 352, 360, 384, 400, 432, 448, 480, 512, 576, 640, 648, 672, 704, 720, 768, 800, 832, 864, 896, 960, 972, 1008, 1024, 1056
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Conway, John H. and Guy, Richard K., The Book of Numbers, Copernicus, 1996, pp. 132-3.
Ore, Oystein, Number Theory and Its History, McGraw-Hill, 1948, (also reprinted 1988), pp. 50-52.
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LINKS
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Walter Nissen, Home Page (listed in lieu of email address)
Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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OMEGA(n) > ln(n), where OMEGA is the total number of prime factors and ln is the natural logarithm.
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EXAMPLE
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a(1) = 2 because 2 has 1 prime factor, viz., 2 and ln ( 2 ) ~= .693 and 1 > .693.
4 is included because sum of exponents in prime factorization of 4 is 2, which is > ln(4).
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CROSSREFS
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Cf. A081209.
Sequence in context: A068563 A124240 A068997 this_sequence A060765 A140110 A128397
Adjacent sequences: A067709 A067710 A067711 this_sequence A067713 A067714 A067715
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet Feb 05 2002
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EXTENSIONS
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More terms from Walter Nissen Mar 10 2003
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