A182147 Numbers n equal to the sum of its proper divisors greater than square root of n.

42, 54, 66, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 812, 822, 834, 868, 894, 906, 942, 978, 1002, 1036, 1038, 1074, 1086, 1146, 1148, 1158, 1182, 1194, 1204, 1266

Offset

1,1

Comments

On a suggestion of Jordi Domènech i Arnau. Is 34155 the only odd number in this sequence?

34155 is the only odd term < 2*10^11. - Donovan Johnson, Apr 18 2012

Also composite numbers such that the sum of the reciprocals of the divisors <= sqrt(n) is an integer. - Michel Lagneau, Mar 03 2014

From Amiram Eldar, Sep 14 2019: (Start)

If k is a perfect number (A000396) and p > k is a prime then k * p is in the sequence.

If p is a Mersenne exponent (A000043) then 2^(p-1) * M(p)^3 is in the sequence, where M(p) = 2^p - 1 is a Mersenne prime (A000668). These terms are 54, 1372, 476656, 131096512, ... (End)

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Discussion on MathForum (in Spanish), March 2003.

Example

The proper divisors of 42 greater than sqrt(42) are 7, 14 and 21, and 7 + 14 + 21 = 42.

Mathematica

d[n_] := Select[Most[Divisors[n]], # > Sqrt[n] &]; Select[Range[2, 2000], # == Total[d[#]] &] (* T. D. Noe, Apr 16 2012 *)

Prog

(Haskell)
a182147 n = a182147_list !! (n-1)
a182147_list = [w | w <- [1..] , sum (dropWhile (<= a000196 w) $
                                      a027751_row $ fromInteger w) == w]
-- Reinhard Zumkeller, Apr 18 2012

Crossrefs

Cf. A000196, A000043, A000396, A000668, A027751, A238535.

Sequence in context: A125009 A008886 A341129 * A029695 A307986 A143226

Adjacent sequences: A182144 A182145 A182146 * A182148 A182149 A182150

Keyword

nonn

Author

Claudio Meller, Apr 14 2012

Status

approved