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A067666
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Sum of squares of prime factors of n (counted with multiplicity).
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12
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0, 4, 9, 8, 25, 13, 49, 12, 18, 29, 121, 17, 169, 53, 34, 16, 289, 22, 361, 33, 58, 125, 529, 21, 50, 173, 27, 57, 841, 38, 961, 20, 130, 293, 74, 26, 1369, 365, 178, 37, 1681, 62, 1849, 129, 43, 533, 2209, 25, 98, 54, 298, 177, 2809, 31, 146, 61, 370, 845, 3481
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OFFSET
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1,2
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COMMENTS
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16 and 27 are fixed points, ... and see Rivera link. - Michel Marcus, Sep 19 2020
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LINKS
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FORMULA
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a(x*y) = a(x) + a(y); a(p^k) = k*p^2 for p prime.
Totally additive with a(p) = p^2.
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EXAMPLE
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a(2) = 2^2 = 4;
a(45) = a(3*3*5) = 3^2 + 3^2 + 5^2 = 43.
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MATHEMATICA
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Join[{0}, Table[Total[Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[ n]]^2], {n, 2, 60}]] (* Harvey P. Dale, Dec 24 2012 *)
Join[{0}, Table[Total[#[[1]]^2*#[[2]] & /@ FactorInteger[n]], {n, 2, 60}]] (* Zak Seidov, Apr 18 2013 *)
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PROG
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(PARI) a(n)=local(fm, t); fm=factor(n); t=0; for(k=1, matsize(fm)[1], t+=fm[k, 1]^2*fm[k, 2]); t \\ Franklin T. Adams-Watters, May 03 2009
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]^2*f[k, 2]); \\ Michel Marcus, Sep 19 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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