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A064001
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Odd abundant numbers not divisible by 5.
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6
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81081, 153153, 171171, 189189, 207207, 223839, 243243, 261261, 279279, 297297, 351351, 459459, 513513, 567567, 621621, 671517, 729729, 742203, 783783, 793611, 812889, 837837, 891891, 908523, 960687, 999999, 1024947, 1054053, 1072071
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OFFSET
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1,1
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COMMENTS
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Or, odd abundant numbers that do not end in 5.
All terms below 2000000 are divisible by 21 (so by 3). Moreover, except for a few, most are divisible by 231. - Labos Elemer, Sep 15 2005
An odd abundant number (see A005231) not divisible by 3 nor 5 must have at least 15 distinct prime factors (e.g., 61#/5#*7^2*11*13*17, where # is primorial) and be >= 67#/5#*77 = A047802(3) ~ 2.0*10^25. -- The smallest non-primitive abundant number (cf. A006038) in this sequence is 7*a(1) = 567567 = a(14). - M. F. Hasler, Jul 27 2016
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REFERENCES
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 169 (Rev. ed. 1997).
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LINKS
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Jay L. Schiffman, Odd Abundant Numbers, Mathematical Spectrum, Volume 37, Number 2 (January 2005), pp 73-75.
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MATHEMATICA
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Select[ Range[ 1, 10^6, 2 ], DivisorSigma[ 1, # ] - 2# > 0 && Mod[ #, 5 ] != 0 & ]
ta={{0}}; Do[g=n; s=DivisorSigma[1, n]-2*n; If[Greater[s, 0]&&!Equal[Mod[n, 2], 0]&& !Equal[Mod[n, 5], 0], Print[n]; ta=Append[ta, n]], {n, 1, 2000000}] ta=Delete[ta, 1] (* Labos Elemer, Sep 15 2005 *)
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PROG
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(PARI) { n=0; forstep (m=1, 10^9, 2, if (m%5 && sigma(m) > 2*m, write("b064001.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 05 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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