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A072370
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Numbers n such that tau(n) = ln(n) + 2 * EulerGamma - 1 (rounded off), where tau(n) denotes the number of divisors of n and EulerGamma denotes the Euler-Mascheroni constant (0.5 is rounded to 0).
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0
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5, 7, 25, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 81, 212, 236, 242, 243, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428, 436, 452, 475, 477, 507, 508, 524, 531, 539, 548
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OFFSET
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1,1
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COMMENTS
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Dirichlet proved that the average value of tau(n) is approximately ln(n) + 2 * EulerGamma - 1 (see the reference by Tattersall).
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REFERENCES
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Tattersall, J. "Elementary Number Theory in Nine Chapters". Cambridge University Press, 1999.
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LINKS
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Table of n, a(n) for n=1..56.
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MATHEMATICA
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Select[Range[10^3], DivisorSigma[0, # ] == Round[Log[ # ] + 2*EulerGamma - 1] &]
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CROSSREFS
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Sequence in context: A166660 A037374 A056717 * A057490 A057253 A003595
Adjacent sequences: A072367 A072368 A072369 * A072371 A072372 A072373
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jul 19 2002
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STATUS
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approved
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