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A067666 Sum of squares of prime factors of n (counted with multiplicity). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(x*y) = a(x) + a(y); a(p^k) = k*p^2 for p prime.

Totally additive with a(p) = p^2.

EXAMPLE

a(2) = 2^2 = 4;

a(45) = a(3*3*5) = 3^2 + 3^2 + 5^2 = 43.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A166319 (where a(n)<=n), A001222, A001414, A005063, A078137, A081403.

Sequence in context: A285109 A217579 A118585 * A280286 A268597 A253560

Adjacent sequences:  A067663 A067664 A067665 * A067667 A067668 A067669

KEYWORD

nonn

AUTHOR

Henry Bottomley, Feb 04 2002

EXTENSIONS

Values through a(59) verified by Franklin T. Adams-Watters, May 03 2009

STATUS

approved

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Last modified May 19 20:41 EDT 2019. Contains 323410 sequences. (Running on oeis4.)