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a(n) = Product_{d|n} (n/d + d).
1

%I #36 May 28 2021 13:09:58

%S 2,9,16,100,36,1225,64,2916,600,5929,144,529984,196,18225,16384,

%T 231200,324,3538161,400,5143824,48400,89401,576,1482250000,6760,

%U 164025,112896,26050816,900,5679280321,1024,50808384,226576,442225

%N a(n) = Product_{d|n} (n/d + d).

%C a(n) is a square when n is not a square or of the form (2m^2)^2 = 4m^4.

%C If n is prime, then a(n) = (n+1)^2. - _Wesley Ivan Hurt_, Apr 19 2021

%H T. D. Noe, <a href="/A045661/b045661.txt">Table of n, a(n) for n = 1..1000</a>

%F a(A006881(n)) = (sopf(A006881(n)) * (A006881(n)+1) )^2. - _Wesley Ivan Hurt_, May 20 2013

%t Times@@(#/Divisors[ # ]+Divisors[ # ])& /@ Range[ 48 ]

%o (Haskell)

%o a045661 n = product [n'+d | d <- [1..n], let (n',m) = divMod n d, m == 0]

%o -- _Reinhard Zumkeller_, Feb 02 2012, Jan 25 2012

%o (PARI) a(n)=my(t=1);fordiv(n,d,t*=n/d+d);t \\ _Charles R Greathouse IV_, Jan 25 2012

%o (PARI) A045661(n)=my(t=1+#n=divisors(n));prod(i=1,(t-1)\2,n[i]+n[t-i])^2*if(bittest(t,0),1,2*n[t\2]) \\ _M. F. Hasler_, Jan 25 2012

%K nonn,nice,easy

%O 1,1

%A _Wouter Meeussen_