A045661 a(n) = Product_{d|n} (n/d + d).

2, 9, 16, 100, 36, 1225, 64, 2916, 600, 5929, 144, 529984, 196, 18225, 16384, 231200, 324, 3538161, 400, 5143824, 48400, 89401, 576, 1482250000, 6760, 164025, 112896, 26050816, 900, 5679280321, 1024, 50808384, 226576, 442225

Offset

1,1

Comments

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

If n is prime, then a(n) = (n+1)^2. - Wesley Ivan Hurt, Apr 19 2021

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

a(A006881(n)) = (sopf(A006881(n)) * (A006881(n)+1) )^2. - Wesley Ivan Hurt, May 20 2013

Mathematica

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

Prog

(Haskell)
a045661 n = product [n'+d | d <- [1..n], let (n', m) = divMod n d, m == 0]
-- Reinhard Zumkeller, Feb 02 2012, Jan 25 2012
(PARI) a(n)=my(t=1); fordiv(n, d, t*=n/d+d); t \\ Charles R Greathouse IV, Jan 25 2012
(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

Crossrefs

Sequence in context: A032211 A032136 A032040 * A369647 A078707 A085332

Adjacent sequences: A045658 A045659 A045660 * A045662 A045663 A045664

Keyword

nonn,nice,easy

Author

Wouter Meeussen

Status

approved