A066177 Numbers n such that sigma(n+1)-sigma(n) = -sigma(n)/d(n), where d(n) denotes the number of divisors of n.

165, 1106, 7006, 11516, 12597, 14882, 16604, 21045, 23541, 39866, 42465, 43172, 46078, 67198, 95588, 118988, 121425, 121797, 200186, 426213, 496226, 557265, 1183545, 1247684, 1340241, 1379024, 2106321, 2199716, 3236877, 3853857, 3933045, 4313145, 4477165, 4512375

Offset

1,1

Comments

These are the n at which the divisor sum, sigma(n), is decreasing at a rate equal to the average divisor size, sigma(n)/d(n).

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Example

sigma(165)-sigma(166) = 288-252 = 36 = 288/8 = sigma(165)/d(165).

Mathematica

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

Crossrefs

Cf. A000005 and A000203 (number and sum of divisors).

Sequence in context: A124409 A241614 A225715 * A184490 A027796 A145055

Adjacent sequences: A066174 A066175 A066176 * A066178 A066179 A066180

Keyword

nonn

Author

Joseph L. Pe, Dec 14 2001

Extensions

More terms from Amiram Eldar, Sep 28 2019

Status

approved