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A066176
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Numbers n such that sigma(n+1)-sigma(n) = sigma(n)/d(n), where d(n) denotes the number of divisors of n.
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1
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135, 147, 189, 753, 2697, 8365, 14577, 16929, 18573, 21093, 38481, 67461, 69285, 99237, 100497, 108134, 144555, 148173, 186081, 253761, 263906, 302589, 536834, 560733, 680043, 1158717, 1239554, 1418121, 1431861, 1520313, 1545255, 1657077
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These are the numbers n at which the divisor sum sigma(n) is increasing at a rate equal to the average divisor size, sigma(n)/d(n).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,336
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EXAMPLE
| sigma(136)-sigma(135) = 270-240 = 30 = 240/8 = sigma(135)/d(135).
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MATHEMATICA
| Select[ Range[ 1, 10^5 ], DivisorSigma[ 1, #+1 ]-DivisorSigma[ 1, # ]==DivisorSigma[ 1, # ]/DivisorSigma[ 0, # ] & ]
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PROG
| (PARI) { n=0; for (m=1, 10^9, if (sigma(m + 1) - sigma(m) == sigma(m)/numdiv(m), write("b066176.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 05 2010]
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CROSSREFS
| Sequence in context: A007251 A038369 A066282 * A025363 A096593 A050215
Adjacent sequences: A066173 A066174 A066175 * A066177 A066178 A066179
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 14 2001
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EXTENSIONS
| More terms from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Aug 21 2006
Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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