This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A195690 Numbers such that the difference between the sum of the even divisors and the sum of the odd divisors is a perfect square. 2

%I

%S 2,6,72,76,162,228,230,238,316,434,530,580,686,690,714,716,756,770,

%T 948,994,1034,1054,1216,1302,1358,1490,1590,1740,1778,1836,1870,1996,

%U 2058,2148,2310,2354,2414,2438,2492,2596,2668,2786,2876,2930,2982,3002,3102

%N Numbers such that the difference between the sum of the even divisors and the sum of the odd divisors is a perfect square.

%C Numbers k such that A002129(k) is a square.

%H Amiram Eldar, <a href="/A195690/b195690.txt">Table of n, a(n) for n = 1..10000</a>

%e The divisors of 76 are { 1, 2, 4, 19, 38, 76}, and (2 + 4 + 38 + 76 ) - (1 + 19 ) = 10^2. Hence 76 is in the sequence.

%p with(numtheory):for n from 2 by 2 to 200 do:x:=divisors(n):n1:=nops(x):s1:=0:s2:=0:for m from 1 to n1 do:if irem(x[m],2)=1 then s1:=s1+x[m]:else s2:=s2+x[m]:fi:od: z:=sqrt(s2-s1):if z=floor(z) then printf(`%d, `,n): else fi:od:

%t f[p_, e_] := If[p == 2, 3 - 2^(e + 1) , (p^(e + 1) - 1)/(p - 1)]; aQ[n_] := IntegerQ[Sqrt[-Times @@ (f @@@ FactorInteger[n])]]; Select[Range[2, 3200], aQ] (* _Amiram Eldar_, Jul 20 2019 *)

%Y Cf. A002129, A195268, A195382.

%K nonn

%O 1,1

%A _Michel Lagneau_, Sep 22 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 14:37 EST 2019. Contains 329999 sequences. (Running on oeis4.)