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A182147 Numbers n equal to the sum of its proper divisors greater than square root of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 7 15:02 EDT 2021. Contains 343650 sequences. (Running on oeis4.)