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A005063 Sum of squares of primes dividing n. 23
0, 4, 9, 4, 25, 13, 49, 4, 9, 29, 121, 13, 169, 53, 34, 4, 289, 13, 361, 29, 58, 125, 529, 13, 25, 173, 9, 53, 841, 38, 961, 4, 130, 293, 74, 13, 1369, 365, 178, 29, 1681, 62, 1849, 125, 34, 533, 2209, 13, 49, 29, 298, 173, 2809, 13, 146, 53, 370, 845, 3481, 38, 3721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

Additive with a(p^e) = p^2.

G.f.: Sum_{k>=1} prime(k)^2*x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Dec 24 2016

From Antti Karttunen, Jul 11 2017: (Start)

a(n) = A005066(n) + 4*A059841(n).

a(n) = A005079(n) + A005083(n) + 4*A059841(n).

a(n) = A005071(n) + A005075(n) + 9*A079978(n).

(End)

Dirichlet g.f.: primezeta(s-2)*zeta(s). - Benedict W. J. Irwin, Jul 11 2018

MAPLE

A005063 := proc(n)

        add(d^2, d= numtheory[factorset](n)) ;

end proc;

seq(A005063(n), n=1..40) ; # R. J. Mathar, Nov 08 2011

MATHEMATICA

a[n_] := Total[FactorInteger[n][[All, 1]]^2]; a[1]=0; Table[a[n], {n, 1, 60}] (* Jean-Fran├žois Alcover, Mar 20 2017 *)

Array[DivisorSum[#, #^2 &, PrimeQ] &, 61] (* Michael De Vlieger, Jul 11 2017 *)

PROG

(PARI) a(n)=local(fm, t); fm=factor(n); t=0; for(k=1, matsize(fm)[1], t+=fm[k, 1]^2); t \\ Franklin T. Adams-Watters, May 03 2009

(Scheme) (define (A005063 n) (if (= 1 n) 0 (+ (A000290 (A020639 n)) (A005063 (A028234 n))))) ;; Antti Karttunen, Jul 10 2017

(Python)

from sympy import primefactors

def a(n): return sum([p**2 for p in primefactors(n)])

print map(a, xrange(1, 101)) # Indranil Ghosh, Jul 11 2017

CROSSREFS

Cf. A000290, A005064, A005065, A005066, A005071, A005075, A005079, A005083, A008472, A059841, A079978.

Cf. A067666, A081403, A048261. - Franklin T. Adams-Watters, May 03 2009

Sequence in context: A210966 A300516 A178147 * A235323 A078615 A197863

Adjacent sequences:  A005060 A005061 A005062 * A005064 A005065 A005066

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Franklin T. Adams-Watters, May 03 2009

STATUS

approved

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Last modified October 19 03:31 EDT 2019. Contains 328211 sequences. (Running on oeis4.)