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

Author

Claudio Meller, Apr 14 2012

Keywords

• nonn

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)

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Discussion on MathForum (in Spanish), March 2003.

Crossrefs

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

Programs

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

Mathematica

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