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A066176
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Numbers k such that sigma(k+1) - sigma(k) = sigma(k)/d(k), where d(k) denotes the number of divisors of k.
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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
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OFFSET
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1,1
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COMMENTS
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These are the numbers k at which the divisor sum sigma(k) is increasing at a rate equal to the average divisor size, sigma(k)/d(k).
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LINKS
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EXAMPLE
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sigma(136) - sigma(135) = 270 - 240 = 30 = 240/8 = sigma(135)/d(135).
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MATHEMATICA
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Select[ Range[ 1, 10^5 ], DivisorSigma[ 1, #+1 ]-DivisorSigma[ 1, # ]==DivisorSigma[ 1, # ]/DivisorSigma[ 0, # ] & ]
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PROG
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(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)) ) } \\ Harry J. Smith, Feb 05 2010
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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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