A066176 Numbers k such that sigma(k+1) - sigma(k) = sigma(k)/d(k), where d(k) denotes the number of divisors of k.

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

Offset

1,1

Comments

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).

Links

Harry J. Smith, Table of n, a(n) for n = 1..336

Example

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

Mathematica

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

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)) ) } \\ Harry J. Smith, Feb 05 2010

Crossrefs

Sequence in context: A038369 A066282 A235809 * A025363 A296451 A096593

Adjacent sequences: A066173 A066174 A066175 * A066177 A066178 A066179

Keyword

nonn

Author

Joseph L. Pe, Dec 14 2001

Extensions

More terms from Robert Gerbicz, Aug 21 2006

Corrected by T. D. Noe, Oct 25 2006

Status

approved