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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
2, 6, 72, 76, 162, 228, 230, 238, 316, 434, 530, 580, 686, 690, 714, 716, 756, 770, 948, 994, 1034, 1054, 1216, 1302, 1358, 1490, 1590, 1740, 1778, 1836, 1870, 1996, 2058, 2148, 2310, 2354, 2414, 2438, 2492, 2596, 2668, 2786, 2876, 2930, 2982, 3002, 3102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

MAPLE

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:

MATHEMATICA

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 *)

CROSSREFS

Cf. A002129, A195268, A195382.

Sequence in context: A103527 A239543 A180982 * A171582 A152885 A295182

Adjacent sequences:  A195687 A195688 A195689 * A195691 A195692 A195693

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 22 2011

STATUS

approved

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Last modified November 19 18:39 EST 2019. Contains 329323 sequences. (Running on oeis4.)