A066176 - OEIS

%I #14 Jun 15 2018 22:03:07

%S 135,147,189,753,2697,8365,14577,16929,18573,21093,38481,67461,69285,

%T 99237,100497,108134,144555,148173,186081,253761,263906,302589,536834,

%U 560733,680043,1158717,1239554,1418121,1431861,1520313,1545255,1657077

%N Numbers k such that sigma(k+1) - sigma(k) = sigma(k)/d(k), where d(k) denotes the number of divisors of k.

%C 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).

%H Harry J. Smith, <a href="/A066176/b066176.txt">Table of n, a(n) for n = 1..336</a>

%e sigma(136) - sigma(135) = 270 - 240 = 30 = 240/8 = sigma(135)/d(135).

%t Select[ Range[ 1, 10^5 ], DivisorSigma[ 1, #+1 ]-DivisorSigma[ 1, # ]==DivisorSigma[ 1, # ]/DivisorSigma[ 0, # ] & ]

%o (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

%K nonn

%O 1,1

%A _Joseph L. Pe_, Dec 14 2001

%E More terms from _Robert Gerbicz_, Aug 21 2006

%E Corrected by _T. D. Noe_, Oct 25 2006