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A235323 Squared sum of the distinct prime factors of n, i.e., sopf(n)^2. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A001414, A008472.

Sequence in context: A300516 A178147 A005063 * A078615 A197863 A087320

Adjacent sequences:  A235320 A235321 A235322 * A235324 A235325 A235326

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jan 05 2014

STATUS

approved

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Last modified May 25 01:23 EDT 2019. Contains 323534 sequences. (Running on oeis4.)