A235323 Squared sum of the distinct prime factors of n, i.e., sopf(n)^2.

0, 4, 9, 4, 25, 25, 49, 4, 9, 49, 121, 25, 169, 81, 64, 4, 289, 25, 361, 49, 100, 169, 529, 25, 25, 225, 9, 81, 841, 100, 961, 4, 196, 361, 144, 25, 1369, 441, 256, 49, 1681, 144, 1849, 169, 64, 625, 2209, 25, 49, 49, 400, 225, 2809, 25, 256, 81, 484, 961

Offset: 1

Author

Wesley Ivan Hurt, Jan 05 2014

Keywords

• nonn

Comments

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

Examples

			a(5) = 25; The only prime factor of 5 is just 5, and so 5^2 = 25.
a(6) = 25; The sum of the prime factors of 6 = 2*3 is 2+3 = 5, and 5^2 = 25.
		

Crossrefs

Cf. A008472 (sopf).

Programs

Mathematica

Prepend[Array[Plus @@ First[Transpose[FactorInteger[#]]]^2 &, 100, 2],
  0]
Join[{0},Table[Total[FactorInteger[n][[All,1]]]^2,{n,2,60}]] (* Harvey P. Dale, Feb 10 2019 *)

Formula

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