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Squared sum of the distinct prime factors of n, i.e., sopf(n)^2.
1

%I #14 Jun 16 2021 19:49:33

%S 0,4,9,4,25,25,49,4,9,49,121,25,169,81,64,4,289,25,361,49,100,169,529,

%T 25,25,225,9,81,841,100,961,4,196,361,144,25,1369,441,256,49,1681,144,

%U 1849,169,64,625,2209,25,49,49,400,225,2809,25,256,81,484,961

%N Squared sum of the distinct prime factors of n, i.e., sopf(n)^2.

%C If n is a prime power p^e, A000961, then a(n) = p^2.

%F a(n) = A008472(n)^2.

%e a(5) = 25; The only prime factor of 5 is just 5, and so 5^2 = 25.

%e a(6) = 25; The sum of the prime factors of 6 = 2*3 is 2+3 = 5, and 5^2 = 25.

%t Prepend[Array[Plus @@ First[Transpose[FactorInteger[#]]]^2 &, 100, 2],

%t 0]

%t Join[{0},Table[Total[FactorInteger[n][[All,1]]]^2,{n,2,60}]] (* _Harvey P. Dale_, Feb 10 2019 *)

%Y Cf. A008472 (sopf).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jan 05 2014