cp's OEIS Frontend

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

%I A182147 #50 Sep 14 2019 06:36:01
%S A182147 42,54,66,78,102,114,138,174,186,222,246,258,282,318,354,366,402,426,
%T A182147 438,474,498,534,582,606,618,642,654,678,762,786,812,822,834,868,894,
%U A182147 906,942,978,1002,1036,1038,1074,1086,1146,1148,1158,1182,1194,1204,1266
%N A182147 Numbers n equal to the sum of its proper divisors greater than square root of n.
%C A182147 On a suggestion of Jordi Domènech i Arnau. Is 34155 the only odd number in this sequence?
%C A182147 34155 is the only odd term < 2*10^11. - _Donovan Johnson_, Apr 18 2012
%C A182147 Also composite numbers such that the sum of the reciprocals of the divisors <= sqrt(n) is an integer. - _Michel Lagneau_, Mar 03 2014
%C A182147 From _Amiram Eldar_, Sep 14 2019: (Start)
%C A182147 If k is a perfect number (A000396) and p > k is a prime then k * p is in the sequence.
%C A182147 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)
%H A182147 Reinhard Zumkeller, <a href="/A182147/b182147.txt">Table of n, a(n) for n = 1..10000</a>
%H A182147 <a href="http://mathforum.org/kb/message.jspa?messageID=1785554">Discussion on MathForum</a> (in Spanish), March 2003.
%e A182147 The proper divisors of 42 greater than sqrt(42) are 7, 14 and 21, and 7 + 14 + 21 = 42.
%t A182147 d[n_] := Select[Most[Divisors[n]], # > Sqrt[n] &]; Select[Range[2, 2000], # == Total[d[#]] &] (* _T. D. Noe_, Apr 16 2012 *)
%o A182147 (Haskell)
%o A182147 a182147 n = a182147_list !! (n-1)
%o A182147 a182147_list = [w | w <- [1..] , sum (dropWhile (<= a000196 w) $
%o A182147                                       a027751_row $ fromInteger w) == w]
%o A182147 -- _Reinhard Zumkeller_, Apr 18 2012
%Y A182147 Cf. A000196, A000043, A000396, A000668, A027751, A238535.
%K A182147 nonn
%O A182147 1,1
%A A182147 _Claudio Meller_, Apr 14 2012